Question

Part A

Calculate the magnitude of the maximum orbital angular momentum Lmax for an electron in a hydrogen atom for states with a principal quantum number of 7.

Express your answer in units of ℏ to three significant figures.

Part B

Calculate the magnitude of the maximum orbital angular momentum Lmax for an electron in a hydrogen atom for states with a principal quantum number of 26.

Express your answer in units of ℏ to three significant figures.

Part C

Calculate the magnitude of the maximum orbital angular momentum Lmax for an electron in a hydrogen atom for states with a principal quantum number of 191.

Express your answer in units of ℏ to three significant figures.

Answer 1

Answer:

Explanation:

A )

$L_{max} = \sqrt{l(l+1)}$ℏ

where l is orbital quantum number

l = n-1 where n is principal quantum no

Given n = 7

l = 7 - 1 = 6

$L_{max} = \sqrt{6(6+1)}$ℏ

= 6.48ℏ

B)

Here

n = 26

l = 26 - 1

= 25

$L_{max} = \sqrt{25(25+1)}$ℏ

= 25.49ℏ

= 25.5ℏ

C )

n = 191

l = 191 - 1

190

$L_{max} = \sqrt{190(190+1)}$

= 190.499ℏ

= 191ℏ