Question

Which state of doubly ionization lithium has the same energy as the ground state energy of hydrogen atom?

Answer 1

Answer:

[n=3]

Explanation:

we know, E = -13.6

also, E = $\frac{E_{o}Z^{2} } {n^{2}}$

Li(Z=3) = $\frac{E_{o} Z^{2}}{n^{2} }$ = $\frac{E_{o} 3^{2}}{n^{2} }$ ........ (1)

H(Z, n =1) = $\frac{E_{o} Z^{2}}{n^{2} }$ = $E_{o}$  ...........(2)

Now, equate equation 1 and 2,

$\frac{E_{o} 3^{2}}{n^{2} }$ = $E_{o}$

-13.6x $\frac{3^{2}}{n^{2} }$ = -13.6

$3^{2}$ = $n^{2}$

Therefore,

n=3.