Question

Calculate the deBroglie wavelength of the electron in a triply ionized beryllium atom when it is orbiting in the following state: n = 5.

Answer 1

deBroglie wavelength, = h/p = h/mv
h is the Planck's constant, h = 6.626 x 10^-34 J s
p is the momentum of the orbiting electrons

From the Bohr's quantization rule,
mvr = nh/2
m, v and r are the mass, velocity and radius of an electron orbiting the nucleus.
h/mv = 2r/n ...(1)

The radius of the nth orbit of an electron is give by the formula
r = n²a/Z
a is the Bohr radius, a = 0.0529 x 10^-9 m.
n = 5, Z = 4
r = 25 x (0.0529 x 10^-9) / 4
0.330625 x 10^-9 m

Substituting r in (1)
h/mv = [2 x (0.330625 x 10^-9)] / 5
= 0.4155 x 10^-9 m (answer)