Question

An electron in a hydrogen atom, after absorbing energy photons, can jump between energy states n₁​ and n₂​ (n₂​>n₁​). Then it may return to the ground state after emitting six different wavelengths in the emission spectrum. The energy of emitted photons is either equal to, less than, or greater than the absorbed photons. Then n₁​ and n₂​ are:

Options:
a. n₁​=1,n₂​=7
b. n₁​=2,n₂​=8
c. n₁​=3,n₂​=9
d. n₁​=4,n₂​=10

Answer 1

The correct answer for the provided question is option a, with n1=1 and n2=7. This is because the total number of possible transitions that can emit six different wavelengths only fits the scenario where the energy states transition from n=1 to n=7.

Step-by-step explanation:

An electron in a hydrogen atom that absorbs energy can transition between different energy states, referred to as energy levels. When an electron jumps to a higher energy state after absorbing a photon, this is known as an electronic absorption transition. These energy levels are denoted by the principal quantum number n.

According to the question provided, the electron can emit six different wavelengths upon returning to the ground state, indicating six possible transitions. The only pair of initial and final energy states that accommodate six possible transitions is from n=2 to n=7, as it allows for the transitions from n=7 to n=6, 5, 4, 3, 2, and 1. Therefore, the correct options are n1=1 and n2=7.