Question

A wavelength of (4.653 , mu m) is observed in a hydrogen spectrum for a transition that ends in the (n_f=5) level. What was (n_i) for the initial level of the electron?

a) (1)
b) (2)
c) (3)
d) (4)

Answer 1

The initial level of the electron (ni) for the transition is approximately 1047.

Step-by-step explanation:

To determine the initial level of the electron (ni) for the transition, we need to use the formula for the wavelengths of hydrogen spectrum lines:

1/λ = R (1/nf² - 1/ni²)

Where λ is the wavelength, R is the Rydberg constant, nf is the final level, and ni is the initial level. Rearranging the formula to solve for ni:

1/ni² = 1/nf² - 1/λR

Substituting the given values:

1/ni² = 1/5² - 1/(4.653 µm)R

1/ni² = 1/25 - 1/(4.653 µm)(1.097x10⁷ m⁻¹)

Calculating the right side of the equation gives us:

1/ni² = 0.04 - 2.144x10⁶

Now, taking the reciprocal of ni²:

ni² = 1/(0.04 - 2.144x10⁶)

ni² = 1.095x10⁶

Taking the square root of ni²:

ni ≈ 1047.40

Therefore, the initial level of the electron (ni) is approximately 1047.