atomic structure assignment

Problem:
For a p-electron, orbital angular moment is
(A) √2h (B) h
(C) √6h (D) 2h Solution:
Orbital angular momentum L = √l ( l + 1 )h where h = h/2π
∴ L for p electron = √1 ( 1 + 1 )h = √2h
∴ (A)

Problem:
For which of the following species, Bohr theory doesn’t apply
(A) H (B) He+
(C) Li2+ (D) Na+
Solution:
Bohr theory is not applicable to multi electron species
∴ (D) Problem:
If the radius of 2nd Bohr orbit of hydrogen atom is r2. The radius of third Bohr orbit will be
(A) 4/9r2 (B) 4r2
(C) 9/4r2 (D) 9r2 Solution: r = n2h2/ 4π2mZe2
∴ r2/r3 = 22/32
∴ r3 = 9/4r2
∴ (C)
Problem:
Number of waves made by an electron in one complete revolution in 3rd Bohr orbit is
(A) 2 (B) 3
(C) 4 (D) 1 Solution:
Circumference of 3rd orbit = 2πr3
According to Bohr’s angular momentum of electron in 3rd orbit is mvr3 = 3h/2π or h/mv = 2πr3/3
By de-Broglie equation,
∴ λ = h/mv
∴ λ = 2πr3/3
∴ 2λr3 = 3λ
i.e. circumference of 3rd orbit is three times the wavelength of electron or number of waves made by Bohr electron in one complete revolution in 3rd orbit is three.
∴ (B) Problem:
The degeneracy of the level of hydrogen atom that has energy - RH/16 is
(A) 16 (B) 4
(C) 2 (D) 1 Solution:
En = - RH/n2
∴ - RH/n2 = - RH/16
i.e. for 4th sub-shell i.e. 1 + 3 + 5 + 7 = 16
∴ Degeneracy is 16 Problem:
An electron is moving with a kinetic energy of 4.55 x 10–25 J. What will be de Broglie wavelength for this electron?
(A) 5.28 x 10–7 m (B) 7.28 x 10–7 m
(C) 2 x 10–10 m (D) 3 x 10–5 m Solution:
KE = mv2 =