Which energy state of doubly ionized lithium `Li^(++)` has the same energy as that of the ground state of hydrogen?

Options

A. n=4
B. n=3
C. n=2
D. n=5

Answer

B

Explanation

The energy in the nth orbit is given by `E_n = (-KZ^2)/(n^2)`
Where Z = atomic number and K is a constant
For hydrogen atom in the ground state n = 1 and Z = 1
`therefore E_1 = -K " " ….(1)`
For `Li^(++) , Z=3`
`therefore E_n=(-K(3)^2)/(n^2) = (-9K)/(n^2) " " ...(2)`
It is given that `E_1 = E_n`
`therefore - K = (- 9K)/(n^2) therefore n^2 = 9 " or " n=3`