The quantum state of a particle can be specified by giving a complete set of qua

Question

The quantum state of a particle can be specified by giving a complete set of quantum numbers (n,l, ml,ms). How many different quantum states are possible if the principal quantum number is n = 4? To find the total number of allowed states, first write down the allowed orbital quantum numbers l, and then write down the number of allowed values of ml for each orbital quantum number. Sum these quantities, and then multiply by 2 to account for the two possible orientations of spin.

What is the maximum angular momentum Lmax that an electron with principal quantum number n = 2 can have?

Explanation / Answer

for n= 4 , allowed l values are 0,1,2,3

numer of ml values for a given l = (2*l +1)

hence for n=4 number of quantum states = 2*((2*0 + 1) + (2*1 + 1) + (2*2 + 1) + (2*3 + 1))

= 2*(1 + 3 + 5 + 7)

= 32

angular momentum = (l*(l+1))^0.5 *(h/2*pi)

for n =2 , lmax = 1

hence maximum orbital angular momentum = (2)^0.5 *(h/2*pi)

= 1.414 *(h/2*pi)

= (1.414 x 6.26 x 10^-34) / (2x3.14) Js

= 1.41 x 10^-34 Js

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