Question

Please answer all questions, thank you in advance!

A) What is the lowest possible energy (in electron volts) of an electron in hydrogen if its orbital angular momentum is ?2 h-bar? Express your answer in electronvolts to three significant figures.

B) What is the largest value of the z component of the orbital angular momentum (in terms of h-bar) for the electron in part A? Express your answer as an integer to one significant figure.

C) What is the smallest value of the z component of the orbital angular momentum (in terms of h-bar) for the electron in part A? Express your answer as an integer to one significant figure.

D) What is the largest value of the spin angular momentum (in terms of h-bar) for the electron in part A? Express your answer using three significant figures.

E) What is the smallest value of the spin angular momentum (in terms of h-bar) for the electron in part A? Express your answer using three significant figures.

Answer 1

Solution:(A) Given: Orbital angular momentum = 2 ---------(1)

As per the formula, Orbital angular momentumm, L = n ............(2)

Comparing equation (1) & (2)-------> we get, n=2

Energy of an electron in Bohr’s orbit is,

E = -13.6 * (z^2/n^2) eV---------(3) ,where z is the atomic number of the atom

Here, atomic number of Hydrogen is 1 so z=1.

Now, putting values of n and z in equation number 3, we can write:

E= -13.6 * (1^2/2^2) eV

= -13.6*(1/4) eV

= -3.4 eV

(B) Now, as Orbital angular momentum is l= 2

So, Total angular momentum is L = = =    

the z-component of the angular momentum given by,

Lcos=Lz=m , where m is an integer varying from ?2 to +2

For maximum value, = (m/L) = (2/) = 35^o approx

Therefore, largest value of z component = L = ^o = 2.0

(c) For minimum value, = (m/L) = (0/) = 90^o  , here m = 0

Therefore, smallest value of z component = L = = 0

(D) For electron, spin = s= 1/2 ,

so, spin angular momentum is given by

S = = /2