Bohr S Model For Hydrogen Atom

According to Bohr's model,

%5Chspace%7B15mm%7D%20mvr%3D%5Cfrac%7Bnh%7D%7B2%20%5Cpi%7D%20%5C%2C%20%5C%2C%20%5C%2C%20%5CRightarrow%20%5C%2C%20%5C%2C%20(mv)%5E2%3D%5Cfrac%7Bn%5E2%20h%5E2%7D%7B4%20%5Cpi%5E2%20r%5E2%7D

%5Chspace%7B15mm%7D%20KE%3D%5Cfrac%7B1%7D%7B2%7D%20mv%5E2%20%3D%5Cfrac%7Bn%5E2%20h%5E2%7D%7B8%5Cpi%5E2%20r%5E2%20m%7D%20%5Chspace%7B25mm%7D%20...(i)

Also, Bohr's radius for H-atom is, r =

n%5E2%20%5C%2C%20a_0

Substituting 'r' in E (i) gives

%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20KE%20%3D%5Cfrac%7Bh%5E2%7D%7B8%20%5Cpi%5E2%20%5C%2C%20n%5E2%20%5C%2C%20a_0%5E2%20m%7D%20%5C%2C%20%5C%2C%20when%20%5C%2C%20n%3D2%2C%20KE%3D%5Cfrac%7Bh%5E2%7D%7B32%20%5C%2C%20%5Cpi%5E2%20%5C%2C%20a_0%5E2%20%5C%2C%20m%7D

Thinking Process The problem is based on frequency dependence of photoelectric emission. When incident light with certain frequency (greater than on the threshold frequency is focus on a metal surface) then some electrons are emitted from the metal with substantial initial speed. When an electron moves in a circular path, then

r%3D%5Cfrac%7Bmv%7D%7BeB%7D%20%5CRightarrow%20%5Cfrac%7Br%5E2e%5E2B%5E2%7D%7B2%7D%3D%5Cfrac%7Bm%5E2v%5E2%7D%7B2%7D

KE_%7Bmax%7D%3D%5Cfrac%7B(mv)%5E2%7D%7B2m%7D%5CRightarrow%20%5Cfrac%7Br%5E2e%5E2B%5E2%7D%7B2m%7D%3D(KE)_%7Bmax%7D

Work function of the metal (W), i.e.

W%3D%20hv-KE_%7Bmax%7D

1.89-%5Coint%3D%5Cfrac%7Br%5E2e%5E2B%5E2%7D%7B2m%7D%5Cfrac%7B1%7D%7B2%7DeV%3D%5Cfrac%7Br%5E2eB%5E2%7D%7B2m%7DeV

[

hv%20%5Crightarrow%201.89%20eV%2C

for the transition on from third to second orbit of H-atom]

%3D%5Cfrac%7B100%5Ctimes10%5E%7B-6%7D%5Ctimes1.6%5Ctimes10%5E%7B-19%7D%5Ctimes9%5Ctimes10%5E%7B-8%7D%7D%7B2%5Ctimes9.1%5Ctimes10%5E%7B-31%7D%7D

%5Coint%3D1.89-%5Cfrac%7B1.6%5Ctimes9%7D%7B2%5Ctimes9.1%7D

%3D1.89-0.79%3D1.1%20eV

High-Yield Trend

Chapter Questions
3 MCQs

Official Solution

Official Solution

Official Solution

Bohr S Model For Hydrogen Atom

High-Yield Trend

Chapter Questions 3 MCQs

Official Solution

Official Solution

Official Solution

Chapter Questions
3 MCQs