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?
Text Solution
AI Generated Solution
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**:
...
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?
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
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 )
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
PRADEEP-ATOMS AND NUCLEI-Additional Exercise question 6
