Question

In ground state of He⊕ ion how much energy is supplied to electron so that second line of balmer series is obtained in its spectrum:-

(a)10.2eV (b)48.36eV (c)51eV (d)None of these
Please give the explanation.

Answer 1

for Balmer's series, $n_1=2$

for first line of Balmer's series, transition will be $n_1=2,n_2=3$

for 2nd line of Balmer's series, transition will be $n_1=2,n_2=4$

so, amount of energy supplied , E = RhcZ²(1/$n_1^2$- 1/$n_2^2$)

or, E = 13.6Z²(1/$n_1^2$- 1/$n_2^2$)eV

for helium, Z = 2

now, E = 13.6 × 2² ( 1/2² - 1/4²)

= 13.6 × 4 ( 1/4 - 1/16)

= 13.6 × 4 × 3/16

= 13.6 × 3/4

= 3.4 × 3

= 10.2 eV

hence, option (A) is correct.