Question

A 12:5 eV electron beam is used to
bombard gaseous hydrogen at room temperature. Upto
which energy level the hydrogen atoms would be
excited ?
Calculate the wavelengths of the first member of
Lyman and first member of Balmer series​

Answer 1

12.5 ev energy used

let upto n it excites

13.6( 1 -1/n^2) = 12.5

(1-1/n^2) = 12.5/13.6 =0.9

1/n^2 = 0.1

n^2 = 10

n less than 4 So it excites upto 3

first member of lyman

1 to 2

1/wavelength = R ( 1- 1/4)

= 1.09 × 10^7 × 3/4

= 0.8175× 10^7

wavelength = 1/0.8175×10^7. = 1.223 × 10^-7

balmer 2 to 3

(1/4 -1/9) = 5/36

above lyman contains 4/3 factor

so multiply by 9 ×3/5 = 27/5

27/5. × 1.223× 10^-7 = 5.4 ×1.223× 10^-7 = 6.604 × 10^-7