The wavelength of the spectral line when the electron in the hydrogen atom undergoes a transition from the energy level 4 to energy level 2 is

Question

The wavelength of the spectral line when the electron in the hydrogen atom undergoes a transition from the energy level 4 to energy level 2 is (A) 486 nm (B) 486 m (C) 486 mathringA (D) 486 cm

Tardigrade Admin · Accepted Answer

According to Rydberg equation (1/λ)=R ((1/x2)-(1/y2)) R =109678 cm-1 ; x=2 y=4 (1/λ)=109678 [(1/4)-(1/16)] =109678 ×(3/16) On solving, λ=486 mn

Q. The wavelength of the spectral line when the electron in the hydrogen atom undergoes a transition from the energy level $4$ to energy level $2$ is

$486 nm$

$486 m$

$486 \overset{˚}{A}$

$486 c m$

According to Rydberg equation
$\frac{1}{λ} = R (\frac{1}{x ^{2}} - \frac{1}{y ^{2}})$
$R = 109678 c m^{- 1}; x = 2 y = 4$
$\frac{1}{λ} = 109678 [\frac{1}{4} - \frac{1}{16}] = 109678 \times \frac{3}{16}$
On solving, $λ = 486 mn$

Q. The wavelength of the spectral line when the electron in the hydrogen atom undergoes a transition from the energy level 4 to energy level 2 is

486nm

486m

486A˚

486cm