Question

The energy levels the electron can occupy in the Be3+ ion can be calculated using the energy level equation. A Be3+ ion with an electron in the n= 4.00 level emitted a photon with a wavelength of 30.4 nm. What is the value of the level n for the new energy?

Answer 1

n = 2

Step-by-step explanation:

We will solve this problem using the Rydberg equation since all the information is given. One has to be very careful in solving for the energy level becuse the numbers are slightly messy as is solving for n.

When the energy of the transition is given in wavelength it is best to use the Rydberg equation in the form:

1/Lambda = Rh x Z² x ( 1/ n₁² - 1/ n₂²)

Lambda= 30.4 x 10 ⁻⁹ m ( 1nm = 1 x 10⁻⁹ m)

Rh = 10973700 m⁻¹

Z = 4 for Be³⁺

1/(30.4 x 10⁻⁹ )= 10973700 x (16) x (1/ n² - 1/4²)=

0.1873 + 1/16 = 1/ n²

n² = 1/ 0.25

n ² = 4

n= √4 = 2