If Bohr's qunatisation postulate (angular momentum=`nh//2pi`) is a basic law of nature, it should be equally valid for the case of planetary motion also. Why then do never speak of quantization of orbits of planets around the sun?
If Bohr's qunatisation postulate (angular momentum=`nh//2pi`) is a basic law of nature, it should be equally valid for the case of planetary motion also. Why then do never speak of quantization of orbits of planets around the sun?
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To understand why we do not speak of the quantization of orbits of planets around the sun, we can analyze the situation step by step.
### Step-by-Step Solution:
1. **Understanding Bohr's Quantization Postulate**:
Bohr's quantization postulate states that the angular momentum of an electron in an atom is quantized and is given by the formula \( L = n \frac{h}{2\pi} \), where \( n \) is a positive integer (quantum number) and \( h \) is Planck's constant.
2. **Application to Planetary Motion**:
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If Bohr’s quantisation postulate (angular momentum = nh//2pi ) is a basic law of nature, it should be equally valid for the case of planetary motion also. Why then do we never speak of quantisation of orbits of planets around the sun?
If Bohar 's quantisation postulate ( angular momentum = nh//2pi ) is a basic law of nature , it should be equal be equally valid for the case of planetary motion also . Why then do we never speak of quatisation of orbit of planets around the Sun ?
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In a hydrogen like ion, nucleus has a positive charge Ze, Bohr's quantization rule is, the angular momentum of an electron about the nucleus l = (nh)/(2pi) , where 'n' is a positive integer. If electron is in ground state the magnetic field produced at the site of nucleus due to circular motion of the electron
In a hydrogen like ion, nucleus has a positive charge Ze, Bohr's quantization rule is, the angular momentum of an electron about the nucleus l = (nh)/(2pi) , where 'n' is a positive integer. If electron is in ground state the magnetic field produced at the site of nucleus due to circular motion of the electron
A
`(mu_(0)Z^(3))/(8pi)(e^(7)m^(2))/(in_(0)^(3)h^(5))`
B
`(mu_(0)Z^(2))/(8pi) (e^(7)m^(2))/(in_(0)^(3)h^(5))`
C
`(mu_(0)piZ^(3))/(8)(e^(7)m^(2))/(in_(0)^(3)h^(5))`
D
`(mu_(0)piZ^(2))/(8) (e^(7)m^(2))/(in_(0)^(3)h^(5))`
The key feature of Bohr'[s spectrum of hydrogen atom is the quantization of angular momentum when an electron is revolving around a proton we will extend this to a general rotational motion to find quntized rotantized rotational energy of a diatomic molecule assuming it to be right . The rate to energy applied is Bohr's quantization condition it is found that the excitation from ground to the first excited state of rotation for the CO molecule is close to (4)/(pi) xx 10^(11) Hz then the moment of inertia of CO molecule about its center of mass is close to (Take h = 2 pi xx 10^(-34) J s )
The key feature of Bohr'[s spectrum of hydrogen atom is the quantization of angular momentum when an electron is revolving around a proton we will extend this to a general rotational motion to find quntized rotantized rotational energy of a diatomic molecule assuming it to be right . The rate to energy applied is Bohr's quantization condition it is found that the excitation from ground to the first excited state of rotation for the CO molecule is close to (4)/(pi) xx 10^(11) Hz then the moment of inertia of CO molecule about its center of mass is close to (Take h = 2 pi xx 10^(-34) J s )
A
`2.76 xx 10^(-46) kg m^(2)`
B
`1.87 xx 10^(-46) kg m^(2)`
C
`4.67 xx 10^(-47) kg m^(2)`
D
`1.17 xx 10^(-47) kg m^(2)`
Consider the following statements regarging Bohr atomic model- 1. It introduces the ideal of stationary orbits. 2. It assumes the angular momentum of electron equal to -((1)/(2))(h)/(2pi) 3. It uses planetary model of the atom involving circular orbits Which of the statements given above are correct?
Consider the following statements regarging Bohr atomic model- 1. It introduces the ideal of stationary orbits. 2. It assumes the angular momentum of electron equal to -((1)/(2))(h)/(2pi) 3. It uses planetary model of the atom involving circular orbits Which of the statements given above are correct?
A
1 and 2
B
2 and 3
C
1 and 3
D
1, 2 and 3
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While studying the theory of planetary motion, kepler established three laws. According to kepler's second law, the line joining a planet to the sun sweeps out equal areas in equal intervals of time, i.e., the areal velocity of the planet around the sun is constant. This led him to conlude from the sun. Read the above passege and answer the following questions : (i) What is the basis of kepler's second law? (ii) Mercury is closer to the sun than the earth. Will time period of mercury be less or more than one year ? Why ? (iii) What value of life do you learn from kepler's second law?
L = sqrt(l(l+1)) (h)/(2pi) On the other hand, m determines Z-component of orbital angular momentum as L_(z) = m ((h)/(2pi)) Hunds rule states that in degenerate orbitals electron s do not pair up unless and until each such orbital has got an electron with parallel spins. Besides orbital motion, an electron also possess spin-motion. spin may be clockwise and anti-clockwise. Both thes spin motions are called two spin states of electron characterised by spin. s = +(1)/(2) and s =- (1)/(2) , respectively. An orbital has n = 5 and its l value is the maximum possible. The orbital angular momentum of the electron in this orbital will be
L = sqrt(l(l+1)) (h)/(2pi) On the other hand, m determines Z-component of orbital angular momentum as L_(z) = m ((h)/(2pi)) Hund's rule states that in degenerate orbitals electron s do not pair up unless and until each such orbital has got an electron with parallel spins. Besides orbital motion, an electron also possess spin-motion. spin may be clockwise and anti-clockwise. Both thes spin motions are called two spin states of electron characterised by spin. s = +(1)/(2) and s =- (1)/(2) , respectively. The orbital angular momentum of electron (l =1) makes an angle of 45^(@) from Z-axis. The L_(z) of electron will be
Planets and comets follow an elliptical path around the Sun, with the Sun lying at one of the foci of the ellipise. This motion is due to the gravitational force of attraction acting between the Sun and the planets (or comets), which is central in nature. This further implies that the angular momentum of a planet moving around the Sun is constant. When a planet is nearer the Sun, it speeds up while it slows down when it is farther away. One could also predict the time period (T) of revolution of a planet from a knowledge of its mean distance (R ) from the Sun i.e., the average of its distances from the Sun at aphellon (farthest point) and perihelion (nearest point), since T^(2) prop R^(3) This equation is also valid for circular orbits and the constant of proportionality is the same for both. A comet of mass m moves around the Sun in closed orbit which takes it to a distance of a when it is closest to the Sun and a distance of 4a when it is farthest from the Sun. Assume that the mass of the Sun is M . It is observed that the total energy ( KE+ gravitational PE ) is conserved. The toal energy of the comet is
Planets and comets follow an elliptical path around the Sun, with the Sun lying at one of the foci of the ellipise. This motion is due to the gravitational force of attraction acting between the Sun and the planets (or comets), which is central in nature. This further implies that the angular momentum of a planet moving around the Sun is constant. When a planet is nearer the Sun, it speeds up while it slows down when it is farther away. One could also predict the time period (T) of revolution of a planet from a knowledge of its mean distance (R ) from the Sun i.e., the average of its distances from the Sun at aphellon (farthest point) and perihelion (nearest point), since T^(2) prop R^(3) This equation is also valid for circular orbits and the constant of proportionality is the same for both. A comet of mass m moves around the Sun in closed orbit which takes it to a distance of a when it is closest to the Sun and a distance of 4a when it is farthest from the Sun. Assume that the mass of the Sun is M . The gravitational potential energyof the comet varies from the aphelion to the perihelion during the course of its revolution. The maximum variation in its kinetic energy is (KE_(max)-KE_(min))