Question

The Li+2 ion contains only one electron and is therefore a hydrogen-like ion that can be described by the Bohr model. Calculate the wavelengths of the lowest energy transitions in the Lyman and Brackett series for the Li+2 ion.

Answer 1

1)

for Lyman series, the lowest energy transition from n=2 to n=1

Here photon will be emitted

1/lambda = R*Z^2* (1/nf^2 - 1/ni^2)

R is Rydberg constant. R = 1.097*10^7

Here Z = 3

1/lambda = R*Z^2* (1/nf^2 - 1/ni^2)

1/lambda = 1.097*10^7*3^2* (1/1^2 - 1/2^2)

lambda = 1.35*10^-8 m

lambda = 14 nm

Answer: 1.35*10^-8 m

2)

for Brackett series, the lowest energy transition from n=5 to n=4

Here photon will be emitted

1/lambda = R*Z^2* (1/nf^2 - 1/ni^2)

R is Rydberg constant. R = 1.097*10^7

Here Z = 3

1/lambda = R*Z^2* (1/nf^2 - 1/ni^2)

1/lambda = 1.097*10^7*3^2* (1/4^2 - 1/5^2)

lambda = 4.50*10^-7 m

lambda = 450 nm

Answer: 4.50*10^-7 m