Question

2. Which of the following electrons will emit light of LONGER WAVELENGTH An electron dropping from n = 3 ton=1 OR an electron dropping from n = 4 ton2? Calculate the wavelength for each transition to justify your answer. given Som [R=1.097410tm-17 21.097 X1o mi -

pls help me with this.
using the equations above
Thanks

Answer 1

Q2. According to Rydberg equation,

1/$\lambda$ = R * (1/n₂² - 1/n₁²)

where

$\lambda$ = wavelength of transition

R = Rydberg constant = 1.097 x 10⁷ m^-1

n₁ > n₂

(a) transition from n = 3 to n = 1

For this transition, n₁ = 3

n₂ = 1

Substituting the values in Rydberg equation,

1/$\lambda$ = (1.097 x 10⁷ m^-1) * (1/(1)² - 1/(3)²)

1/$\lambda$ = (1.097 x 10⁷ m^-1) * (1 - 0.111)

1/$\lambda$ = (1.097 x 10⁷ m^-1) * (0.889)

1/$\lambda$ = 9.75 x 10⁶ m^-1

$\lambda$ = 1/(9.75 x 10⁶ m^-1)

$\lambda$ = 1.0255 x 10^-7 m

$\lambda$ = 1.0255 x 10^-7 m * (1 x 10⁹ nm / 1 m)

$\lambda$ = 102.55 nm

(b) transition from n = 4 to n = 2

For this transition, n₁ = 4

n₂ = 2

Substituting the values in Rydberg equation,

1/$\lambda$ = (1.097 x 10⁷ m^-1) * (1/(2)² - 1/(4)²)

1/$\lambda$ = (1.097 x 10⁷ m^-1) * (0.25 - 0.0625)

1/$\lambda$ = (1.097 x 10⁷ m^-1) * (0.1875)

1/$\lambda$ = 2.057 x 10⁶ m^-1

$\lambda$ = 1/(2.057 x 10⁶ m^-1)

$\lambda$ = 4.862 x 10^-7 m

$\lambda$ = 4.862 x 10^-7 m * (1 x 10⁹ nm / 1 m)

$\lambda$ = 486.2 nm

Since value of wavelength is higher in transition from n = 4 to n = 2, therefore, this transition will emit light of longer wavelength.