Question

A hydrogen atom is in the n = 3 state. Determine, according to quantum mechanics, (a) the total energy (in eV) of the atom, (b) the magnitude of the maximum angular momentum the electron can have in this state, and (c) the maximum value that the z component Lz of the angular momentum can have.

Answer 1

Explanation:

Given that,

Number of state = 3

(a). We need to calculate the total energy

Using formula of the total energy

$E=-\dfrac{13.6\timesz^2}{n^2}$

Put the value of n

$E=\dfrac{-13.6\times1}{3^2}$

$E=1.511\ eV$

(b). L= n-1= 3-1 = 2

Using formula of angular momentum

$J=\dfrac{h}{2\pi}\sqrt{l(l+1)}$

$J=\dfrac{6.6\times10^{-34}}{2\pi}\times\sqrt{2(2+1)}$

$J=2.572\times10^{-34}\ J-s$

(c). Maximum value l =2

We need to calculate the the angular momentum

$J=\dfrac{2h}{2\pi}$

$J=\dfrac{2\times6.6\times10^{-34}}{2\pi}$

$J=2.100\times10^{-34}\ J-s$

Hence, This is required solution.