Question

a) Show that the circumference of Bohr’s orbit for the H-atom is an integral
multiple of the de-Broglie wavelength of electron revolving around the orbit.
b) When a photon of frequency 1.0 x 1015
s
-1 was allowed to hit a metal
surface, an electron having 1.988 x 10-19J of kinetic energy is emitted.
Calculate the threshold frequency of this metal. Show that an will not be
emitted if a photon with a wavelength equal to 600 nm hits the metal
surface.

Answer 1

Answer:

(a). true

(b). false

(c). false

(d). true

Answer 2

Answer (a).

expression for the angular momentum is

mvr=

2π

nh

, or 2πr=

mv

nh

......(i)

The wavelength is given by the De Broglie's equation.

λ=

mv

m

.....(ii)

From (i) and (ii), we have

2πr=nλ

Hence, the circumference of the Bohr orbit for the hydrogen atom is an integral multiple of the de Broglie's wavelength associated with the electron revolving around the orbit.