When R is Rydbergs constant for hydrogen, the wave number of the first line in the Lyman series is:

Question

When R is Rydbergs constant for hydrogen, the wave number of the first line in the Lyman series is: (A)  (R/4)  (B)  (3R/4)  (C)  (R/2)  (D)  2R

Tardigrade Admin · Accepted Answer

When an electron in an atom jumps from higher orbits to the ground orbit, Lyman series is found. The wavelength of lines obtained in Lyman series is given by

\frac{1}{λ} = R (\frac{1}{1 ^{2}} - \frac{1}{n ^{2}}) n = 2, 3, 4, .....

For first line of Lyman series,

n = 2

∴

\overset{v}{ˉ} = \frac{1}{λ _{1}} = R (\frac{1}{1 ^{2}} - \frac{1}{2 ^{2}})

or

= R (\frac{4 - 1}{4})

or

\overset{v}{ˉ} = \frac{3 R}{4}

Note: For shortest wavelength of Lyman series, put

n = \infty.

Q. When R is Rydbergs constant for hydrogen, the wave number of the first line in the Lyman series is:

$\frac{R}{4}$

$\frac{3 R}{4}$

$\frac{R}{2}$

$2 R$

Q. When R is Rydbergs constant for hydrogen, the wave number of the first line in the Lyman series is:

4R​

43R​

2R​

2R

$\frac{R}{4}$

$\frac{3 R}{4}$

$\frac{R}{2}$

$2 R$