difference between rutherford and bohr model

But opting out of some of these cookies may affect your browsing experience. Copyright 2023 WisdomAnswer | All rights reserved. Difference Between Rutherford and Bohr Model, What is the Difference Between Rutherford and Bohr Model. Most of the fast moving alpha-particles passed straight through the gold foil. It does not adhere to the Heisenberg Uncertainty Principle. The core contains all of the atoms mass. How are the Bohr model and the Rutherford model of the atom similar? Post navigation Rutherfordsrd model could not explain the. 3)Rutherford's model states that atom consists with a central core where almost whole mass is concentrated. Rutherford explained the nucleus of an atom and Bohr modified that model into electrons and their energy levels. These orbit shells as indicated by Rutherford-Bohr theory shows that they have different energy levels and have a spherical shape. Comparison between Rutherford's model and Bohr's model: (i) Rutherford describes the atom as a tiny dense, positivity charged cored called a nucleus, in which nearly all the mats are concentrated. Bohr model observation is based on the line of spectra of the hydrogen atom whereas Rutherford model observation are based on gold foil experiment The electrons can have only specific amounts of energy. Home Science Chemistry General Chemistry Difference Between Rutherford and Bohr Model. Bohr model was proposed by Niels Bohr in 1915. What are the functions of the base and the arm of the microscope Kabuuang mga Sagot: 1. magpatuloy. eleanorrigby-movie.com 2023 He explained the laws of the chemical combination by considering atoms as invisible particles without a structure. In this article, we are going to discuss the atomic models of Bohr and Rutherford, similarities between Bohr model and Rutherford model, the evolution and practical results of Bohr model and Rutherford model, and finally the differencebetween Bohr model and Rutherford model. But instead of straight penetration, alpha particles turned into different directions. The main difference between Rutherford model and Bohr model is that Rutherford model does not explain the energy levels in an atom whereas Bohr model explains the energy levels in an atom. Necessary cookies are absolutely essential for the website to function properly. The transfer of electrons is possible by emission and absorption of energy. Earnest Rutherford and Niels Bohr are two prominent scientists who contributed to the field of physics greatly. It cannot predict the relative intensities of spectral lines. Emission of radiations of electrons is of specific frequencies, Emission of radiations of electrons is of all frequencies. Rutherford had discovered the nuclear atom, a small, positively-charged nucleus surrounded by empty space and then a layer of electrons to form the outside of the atom. 3)Rutherfords model states that atom consists with a central core where almost whole mass is concentrated. Both Rutherford model and Bohr model explain the same concept of atomic structure with slight variations. If you would like to change your settings or withdraw consent at any time, the link to do so is in our privacy policy accessible from our home page.. Madhusha is a BSc (Hons) graduate in the field of Biological Sciences and is currently pursuing for her Masters in Industrial and Environmental Chemistry. Observations found on Rutherford's model : 1. Side by Side Comparison Bohr vs Rutherford Model in Tabular Form. He suggested that electrons could revolve around the nucleus in only certain orbits; each orbit having a different radius. Bohr model observation is built on the line spectra for the hydrogen atom, while Rutherford model observation are built on gold foil experiment Bohrs model is able to explain the spectrum of the hydrogen atom, but it cannot fully explain the reactivity of multielectron atoms. He gave his theory of the structure of the atom in 1911 that stated that the majority of the atom's mass is located in a compact, positively charged area in the center of the atom. The year 1913 brought the Bohr model of the hydrogen atom, which made use of the quantum to explain the atomic spectrum although at the time Bohr did not believe the atom to be wave-like but like a solar system so . Bohr model observation is based on the line of spectra of the hydrogen atom whereas Rutherford model observation are based on gold foil experiment, Rutherford model does not explain the presence of discrete energy levels while the Bohr model explains the presence of discrete energy levels, Bohr model provides a relationship between orbit energy and size whereas the Rutherford model does not offer a description between orbit energy and size, Bohr model emission occurs in the line of the spectrum whereas the Rutherford model is a continuous spectrum. The main difference between Bohr model and Rutherford model is that in Rutherford model, electrons can revolve in any orbit around the nucleus, whereas in Bohr model, electrons can revolve in a definite shell. eNotes Editorial, 22 Nov. 2015, https://www.enotes.com/homework-help/what-similarities-differences-between-bohr-atom-548418. Complete Step by step solution: - Bohr's model of the atom was based on quantum theory where the electrons move around the nucleus in definite orbits. Stop procrastinating with our smart planner features. To provide an explanation, the primary purpose of this experiment was to observe how alpha particles were reflected through gold foil. In 1912, Niels Bohr thought about Rutherford's model and, given what he understood about the laws of quantum physics, concluded that the nuclear model would not be . Some of our partners may process your data as a part of their legitimate business interest without asking for consent. Save my name, email, and website in this browser for the next time I comment. Thomson discovered electrons using a cathode ray tube and developed his plum pudding model. 2)Rutherford's model do not deals with discrete energy levels. Niel Bohr's Atomic Theory states that - an atom is like a planetary model where electrons were situated in discretely energized orbits. In this model, Bohr mentioned that the most of the atomic mass lies in the central nucleus that contains protons and electrons are arranged in definite energy levels and revolve around the nucleus. Main Difference between Bohr and Rutherford Model Bohr model was postulated in 1922 whereas the Rutherford model in 1913. In this view, electron orbits around the nucleus resemble that of planets around the sun in the solar system. However, a French physicist, de Broglie discovered that electronshave both wave and particle properties. Find the wavelength of the spectra of any hydrogen-like atom with our Rydberg equation calculator. Niels Bohr changed the atomic theory by creating the Bohr model of the atom. Rutherford model and Bohr model are models that explain the structure of an atom. In the Bohr model, the electrons' orbits are at fixed discrete distances from the nucleus, and in the Rutherford model, the orbits vary in their distance from the nucleus. The expected results were that all the alpha particles would pass the foil without any disturbance. @media (max-width: 1171px) { .sidead300 { margin-left: -20px; } } What did Bohrs model of the atom do that? Surprisingly, it was dimensional analysis that lead him to Planck's theory. Postulation for Rutherford Atomic Model Using Gold Foil Experiment. Rutherfords model states that most of the atom consists of an empty space and the center of the atom contains a positively charged nucleus surrounded by negatively charged electrons, resulting in continuous electron spectrum. Bohr Model: Bohr model explains the relationship between orbital size and the energy of the orbital; smallest orbital has the lowest energy. J.J. Thomson was the first to discover the subatomic particle called electron in 1904. He pictured in his model that electrons are in motion around the nucleus. Our summaries and analyses are written by experts, and your questions are answered by real teachers. In physics the Bohr Model, still commonly used and taught today because of its simplicity, depicts the atom as a small positively charged nucleus with electrons in orbit at different levels, similar in structure to the solar system. Bohr model observation is built on the line spectra for the hydrogen atom, while Rutherford model observation are built on gold foil experiment. Lightweight particles move around the central core. Rutherford model, also called Rutherford atomic model, nuclear atom, or planetary model of the atom, The Rutherford model was devised IN 1911 by the New Zealand-born physicist ERNEST RUTHERFORD to describe an ATOM.. Certain theories such as electromagnetic theory presented by Maxwell could not be explained with Rutherfords model. Overview and Key Difference 2. document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); 2023 Coredifferences.com is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to amazon.com. The shell closest to the nucleus is . Some differences between the Bohr model and the Rutherford model of atom are. Overview and Key Difference The atomic theory was postulated by a Danish Physicist known as Neil Bohr in 1922. Does not follow the Heisenberg Uncertainty Principle. This model is more advanced than Rutherford model which does not describe the movement of electrons along electron shells around the nucleus. Here is the essence of the Bohr model. In fact, according to Rutherfords model, each individual atom should produce a continuous line spectrum. The main difference between Bohr model and Rutherford model is that in Rutherford model, electrons can revolve in any orbit around the nucleus, whereas in Bohr model, electrons can revolve in a definite shell. Rutherford model is based on the experiments Rutherford conducted in collaboration with Geiger and Marsden. Read this quick article for a journey in the lego bricks of matter. According to Rutherfords model, electrons may move anywhere within the volume of space around the nucleus. Describe the development of early atomic theory, including contributions from Dalton, Thomson, Rutherford, Bohr, andSchrdinger. Bohr model was proposed byNiels Bohr in 1922. Overview and Key Difference 2. He concluded that an atomic has specific, allowable energy levels called stationary states in which electrons occupy a fixed circular orbit around the nucleus. Both terms can be used in different ways in a sentence, and everyone knows that soy can be, Read More Difference between Soy and EstoyContinue, You have probably heard the terms observation and inference used several times in statistics. As per Rutherfords model, electrons revolve around the nucleus in a circular path. What is the Difference Between Free Radicals and What is the Difference Between Organic and Inorganic What is the Difference Between Anionic and Nonionic What is the Difference Between Turgor Pressure and What is the Difference Between Phospholipase A and What is the Difference Between Peripheral Nerve and Spinal Nerve, What is the Difference Between Riboflavin and Riboflavin 5 Phosphate, What is the Difference Between Inulin and Psyllium Fiber, What is the Difference Between Holobranch and Hemibranch, What is the Difference Between Mycoplasma Hominis and Genitalium, What is the Difference Between Free Radicals and Reactive Oxygen Species. Bohr atomic model proposes the presence of energy levels whereas Rutherford atomic model does not provide an explanation of orbital shells of atoms. Rutherfords gold foil experiment was the catalyst for this research. Rutherford Model of Atom class 9; Postulates of Bohr Atomic Model; Difference between Rutherford and Bohr Model; De Broglie Concept of Dual Nature of Electron; What are the 4 Principal quantum numbers? BECAUSE OF THE _____ RELATIONSHIP BETWEEN FREQUENCY AND WAVELENGTH, WHEN THE WAVELENGTH OF ENERGY _____, THE ENERGY OF PHOTONS FROM THAT SOURCE _____. biology In his experiments, J.J. Thomson discovered a tiny stream of particles. With our Essay Lab, you can create a customized outline within seconds to get started on your essay right away. This model was proposed in 1913 by Niels Bohr and was really an expansion on the Rutherford model of 1911. Bohr made restrictions on the movement of electrons by imposing pictures of electrons in an orbit around the nucleus. Enthalpy of Fusion of n-Carboxylic Acids? The key difference between Bohr and Schrodinger model is that in the Bohr model, electrons are particles that occupy only certain orbits of fixed energy around the nucleus, whereas, in the Schrodinger model, electrons behave as standing waves having a greater probability of being in some areas of space compared to others. However, it did not give any information about the motion of the electrons. Bohr's model incorporated the then nascent quantum theory in that the distance between electron orbits was fixed, or quantized, and electrons traveling from one orbit to another absorbed or emitted these quanta of energy. However, there are slight differences in the way that they distinguish. The center of the atom contains a positively charged nucleus and its negatively charged electrons are present in the space surrounding the nucleus. Tarendash, A. S. Lets review: chemistry, the physical setting. This gave Rutherford an implication of scattered electrons around the nucleus which is called electron clouds. Figure 1: Structure of Atom as Suggested by Rutherford. The Bohr model of the atom is a classical model of the atom, but it was the first atomic model in which it was proposed that electrons could only occupy specific orbits, called stable orbits.. Key Difference - Bohr vs Rutherford Model The concept of atoms and their structure was first introduced by John Dolton in 1808. Electrons can jump from one orbit to another by emitting or absorbing energy. Paul Flowers, Klaus Theopold, Richard Langley. Let's find out how to calculate the energy difference between orbits. Accessed 4 Mar. The theory states that electrons are always traveling in the orbit shells or orbit around the nucleus. How was Bohr's model similar to Rutherford's? 2)Rutherfords model do not deals with discrete energy levels. What is quantum mechanical model explain? Bohr theory contains small, negatively charged electrons that revolve around a positively charged nucleus. relation between orbital size and the energy of. It does not show that the atom has a nucleus. Which atom and/or ion is (are) isoelectronic with \(\begin{aligned}{{}{}}{{\bf{B}}{{\bf{r}}^ + }:{\rm{ }}{\bf{S}}{{\bf{e}}^{{\bf{2}} + }},{\rm{ }}{\bf{Se}},{\rm{ }}{\bf{A}}{{\bf{s}}^--},{\rm{ }}{\bf{Kr}},{\rm{ }}{\bf{G}}{{\bf{a}}^{{\bf{3}} + }},{\rm{ }}{\bf{C}}{{\bf{l}}^--}?}\\\;\end{aligned}\). Ernest Rutherford. Coming from Engineering cum Human Resource Development background, has over 10 years experience in content developmet and management. It does not predict the relative intensities of spectral lines. Learning objectives covered by this test are listed below. Why Is My Jeep Wrangler Jerking While Accelerating? Ernest Rutherford was the scientist who discovered the atomic model in 1913. It does not explain the Zeeman Effect. On a human scale, matter is as solid as something can be. These cookies will be stored in your browser only with your consent. Does not provide a clear description of the spectra of larger atoms, Atoms are present in the nucleus and they are positively charged, The nucleus of the atom is surrounded by negatively charged particles, Not suitable for explaining the electromagnetic theory, Unclear explanation about the line of spectrum and stability of an atom, Poor description of the electrons arrangement. Continue with Recommended Cookies. Sign up for free to discover our expert answers. What is the difference between Rutherford and Bohr model? It is an atomic theory that is the modification of the Rutherford model. The difference between the energies of those orbits would be equal to the energy of the photon. He fixed and approximately located the presence of electrons in orbital surrounding by using quantum mechanics principles. The formula you met in the Bohr model calculator is strikingly similar to the equation that first explained the spectral lines in hydrogen and hydrogen-like atoms: learn more about the first experimental observations of quantum phenomena with our Rydberg equation calculator. In brief the comparison between Rutherfords and Bohrs model . Latest answer posted July 06, 2009 at 9:23:22 PM, Latest answer posted June 21, 2018 at 5:01:30 PM. Rutherfords model could not explain the presence of the discrete energy level but Bohrs model did. The energy of an orbit is related to the size of the orbit. Bohr model describes about discrete energy levels. The Rutherford gold foil experiment spearheaded the research. In this experiment, a very thin gold foil was bombarded with a beam of alpha particles. These atomic models provide a deeper scientific explanation of the atoms properties. Bohr model is associated with hydrogen line spectrum. He confirmed the existence of protons. electron occupies a large space of an atom. What are the difference between bohr model and rutherford model? Ernest Rutherford is the scientist behind the discovery of the atomic model in 1913. 3 What are some problems with the Bohr model? Bohr model can explain energy levels within an atom, while Rutherford model cannot. Some differences between the Bohr model and the Rutherford model of atom are, Rutherford'srd model could not explain the relation between orbital size and the energy of orbitals. An atom is made up of three particles: electrons, protons, neutrons. Bohr model is associated with hydrogen line spectrum. He kept the positively charged nucleus part the same but he further defined the negatively charged space surrounding it as electrons of tiny comparative mass that orbit the central core in defined rotational orbits similar to the solar system (planets around the Sun). What goes on the bohr diagram? The Bohr model and the Rutherford model are very important in understanding the nature of an atom. 3)Rutherford's model states that atom consists with a . Bohr diagrams show electrons orbiting the nucleus of an atom somewhat like planets orbit around the sun. In atomic physics, the Bohr model or Rutherford-Bohr model of the atom, presented by Niels Bohr and Ernest Rutherford in 1913, consists of a small, dense nucleus surrounded by orbiting electrons.It is analogous to the structure of the Solar System, but with attraction provided by electrostatic force rather than gravity.In the history of atomic physics, it followed, and ultimately replaced . Bohr model also fitted the Einstein model for the photoelectric model: it's no surprise that the equation you can meet on our photoelectric effect calculator is similar to the one above! Bohr was the first to discover that electrons travel in separate orbits around the nucleus and that the number of electrons in the outer orbit determines the properties of an element. Protons and Neutrons are held together in the nucleus by a strong force called . He performed a famous experiment whereby atomic particles were passed through gold foil to measure their mass and size. Poor spectral predictions are obtained when larger atoms are in question. what are the differences between the Rutherford and Bohr models of the atom? What are the three parts of the cell theory? About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket Press Copyright . Functional cookies help to perform certain functionalities like sharing the content of the website on social media platforms, collect feedbacks, and other third-party features. The primary purpose of the experiment was to observe the deflection of alpha particles through the gold foil to provide a clear explanation. Log in here. Atoms with complete electron configurations are not active. In 1913, Danish physicist Niels Bohr applied Max Planck's quantum theory to the nuclear atom of Ernest Rutherford, thus formulating the well-known planetary model of the atom, wherein electrons orbit a central nucleus in well-defined levels of energy ( Figure 1 ). Describe the presence of discrete energy levels. To remedy the stability problem, Bohr modified the Rutherford model by requiring that the electrons move in orbits of fixed size and energy. What was the difference between Thomsons and Rutherfords models of the atom explain how Rutherford was able to refute Thomsons model? Bohr described the hydrogen atom in terms of an electron moving in a circular orbit about a nucleus. In the Bohr model of the atom, electrons travel in defined circular orbits around the nucleus. Both of these models advocated that the electron revolves around the nucleus and occupies a large space in an atom. Most Popular Side by Side Comparison Bohr vs Rutherford Model in Tabular Form Rutherford's Model This video explains Rutherford's model and its limitations. But the observations showed otherwise. Thomson gave the nature of electron, Rutherford the nuclear model of atom, Bohr, the quantum mecha. You can differentiate between sequence and, Read More Difference between Sequence and SeriesContinue, The descriptive statistics is the set of statistical methods that describe and / or characterize a group of data. You can download PDF version of this article and use it for offline purposes as per citation notes. It does not offer an explanation of the relationship between orbital size and energy. Can banks make loans out of their required reserves? How can I download Tekken 7 on Windows 7? The line spectra of hydrogen atom had many discrete lines. Follow this post to learn it. Latest answer posted December 07, 2018 at 12:04:01 PM. The structure of an atomic is explained using the Rutherford model and Bohr model. Unit 2 Review Questions Fill in the blank In a(n) change, a new. These orbit shells, as per Rutherford-Bohr theory, have different energy levels and a spherical form. Bohrs model was proposed by Niels Bohr in 1922 to explain the structure of the atom. Rutherford Model: Rutherford model was developed based on observations of gold foil experiment. Atomic model The Bohr model shows the atom as a small, positively charged nucleus surrounded by orbiting electrons. In his theory, he used the quantum rule which was introduced by Max Planck. 1. The Bohr model utilized the Rydberg formula to explain the spectral lines of hydrogen atoms. In an address to the Physical Society of Copenhagen, Bohr stated, "It can be seen that it is . What are the four basic functions of a computer system? l. A Bohr diagram shows electrons in orbits about the nucleus. This model was proposed based on the line spectra of the hydrogen atom. (CC BY-SA 3.0) via Commons Wikimedia. Summary. (ii) According to Rutherfords model, the electrostatic attraction between electrons and the nucleus was likened to the gravitational force of attraction which implied the structure of a solar system. What is the Bohr Model of the Atom? ThoughtCo, Available here.3. This is a unit test covering the concept of the atom, subatomic particles and their discovery (cathode ray experiment, gold foil experiment, beryllium beam), atomic models (Rutherford, Bohr, quantum), the mole, and mole-gram-atom calculations. Bohr thought that electrons orbited the nucleus in quantized orbits. E_1 E 1. . 1. The main difference between Bohr model and Rutherford model is that in Rutherford model, electrons can revolve in any orbit around the nucleus, whereas in Bohr model, electrons can revolve in a definite shell. Let us know your assignment type and we'll make sure to get you exactly the kind of answer you need. All rights reserved. About 1 particle from 7000 deviated from the original path. Bohr model is a modification of the Rutherford model. chemistry Behavior of Electrons: Part 3, The Bohr Model of the Atom - YouTubeWe combine our new . He pictured in his model that electrons are in motion around the nucleus. The energy difference between the initial and final orbit is emitted by the atom in bundles of electromagnetic radiation called photons. The second flaw to his model was the fact that electrons orbit the nucleus in a circular fashion. Bohr model of the atom. E two is equal to negative 3.4, and E three is equal to negative 1.51 electron volts. Both Bohr and Rutherford models are planetary models that explain the atomic structure up to a certain extent. All the three scientists cited above worked on the understanding of the nature of matter at atomic and subatomic level. 1. Electrons move around the orbit shells or energy levels. increasing radius: \({\bf{A}}{{\bf{s}}^{{\bf{3}}--}},{\rm{ }}{\bf{B}}{{\bf{r}}^--},{\rm{ }}{{\bf{K}}^ + },{\rm{ }}{\bf{M}}{{\bf{g}}^{{\bf{2}} + }}\) . This cookie is set by GDPR Cookie Consent plugin. The radius of the orbit depended on the amount of energy the electron had. Furthermore, Bohr model explained that electrons in one orbital can move to different orbital by either absorbing energy or releasing energy. Comparison between Rutherfords model and Bohrs model: (i) Rutherford describes the atom as a tiny dense, positivity charged cored called a nucleus, in which nearly all the mats are concentrated. Bohr model can be considered a modification to Rutherford model. Rutherford model suggested a new look into the nature of the nucleus, whereas the Bohr model suggested a new look into the mechanics of electrons. What are the Characteristics of P-block Elements? The basic differences between Rutherford and Bohr's Atomic model are. As a modification of Rutherford's model, Bohr explained that electrons move about within fixed orbital shells. What is one sentence to describe the contributions of John Dalton, J.J. Thomson, Ernest Rutherford and Niels Bohr to the atomic theory. So instead of asking describe the main difference between the Bohr model of the atom and the Rutherford model. Energy Levels: Rutherfords model does not deal with detached energy levels besides the Bohr model describes detached energy levels. Rutherford Model:Rutherford model states that an atom is composed of a central core where nearly the whole mass of that atom is concentrated, and light weight particles move around this central core. It was also found that one out of every 12000 particles appeared to rebound. Available here. The nucleus is positively charged and the electron orbit around the nucleus. In 1909, Ernest Rutherford performed his gold foil experiments, which led to the discovery that atoms have a small, dense, positively-charged nucleus. This central positively charged core (which we now term the nucleus) was surrounded by empty space and negative charge, although Rutherford was not specific about this part of the atom. Bohr model suggested that the electrons of an atom traveled in circular orbits around the central nucleus. Observation: Rutherfords model is based on gold foil experimentation and the Bohr model is related to the hydrogen line spectrum. Rutherford Model: Rutherford model does not explain the relationship between orbital size and the energy of the orbital. Performance cookies are used to understand and analyze the key performance indexes of the website which helps in delivering a better user experience for the visitors. Bohr model emission is in the line of spectrum, while Rutherford model emits in continuous spectrum. What is the difference between Bohr and Rutherford? Niels Bohr Planetary Model. Rank the following items in order from largest to smallest: cell, chromosome, gene, DNA, organism, nucleus. How are they different? Since the quantization of momentum is adequately introduced, the model can be considered transactional in that it falls between classical and quantum mechanics. Energized ElectronsPhotons. What Is the Difference between Effector and Memory Cells? The consent submitted will only be used for data processing originating from this website. Key Differences Between Bohr and Rutherford's Atomic Theory Given points are the critical one to understand the difference between two theories: Rutherford's theory says that in the center of an atom is a small positively charged nucleus, which is surrounded by negatively charged electrons. One such limitation is the inability to explain the Zeeman effect and Stark effect observed in line spectra. Rutherford model suggested a new look into the nature of the nucleus, whereas the Bohr model suggested a new look into the mechanics of electrons. Advertisement cookies are used to provide visitors with relevant ads and marketing campaigns. The presence of discrete energie levels is not explained by the Rutherford model, while the Bohr model does. Latest answer posted September 19, 2015 at 9:37:47 PM. Most of the atom consists of empty space. The key difference between Bohr and quantum model is that Bohr model states that electrons behave as particles whereas quantum model explains that the electron has both particle and wave behavior. 2)Rutherford's model do not deals with discrete energy levels. We can calculate an electronic transition energy the difference in energy between two allowed orbits with a straightforward formula: \Delta E = E_2 - E_1 = h \cdot f E = E 2 E 1 = h f. Where: E 1. The Rutherford atomic model states that the atom consists of a central core and the whole mass of the atom is centrally located in the core. The principal difference between the atom-models proposed by Thomson and Rutherford consists in the circumstance the forces acting on the electrons in the atom-model of Thomson allow of certain configurations and motions of the electrons for which the system is in a stable . What are the similarities and differences between the Bohr model and the quantum mechanical model? This cookie is set by GDPR Cookie Consent plugin.

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difference between rutherford and bohr model