In which of the following cases is the frequency of emitted radiation greatest?
Electrons jump from third to second orbit
Electrons jump from fourth to second orbit
Electrons jump from first to second orbit
Electrons jump from third to first orbit
E=hf => Electrons jump from third to first orbit
To determine the case in which the frequency of emitted radiation is greatest, we need to understand a concept called energy levels in an atom.
Energy levels in an atom are like orbits or shells where electrons can exist. Electrons can move between these energy levels by absorbing or emitting energy in the form of light or electromagnetic radiation.
Energy levels in an atom are labeled with integers. The lowest energy level is labeled as n = 1, the second energy level is labeled as n = 2, the third energy level is labeled as n = 3, and so on.
The frequency of the emitted radiation is directly proportional to the energy difference between the initial and final energy levels of the electrons. Higher energy difference means higher frequency.
Now let's analyze the given cases:
1. Electrons jump from the third orbit to the second orbit: In this case, the electrons are moving from a higher energy level (n = 3) to a lower energy level (n = 2), resulting in an energy difference. However, this energy difference is smaller than in some other cases.
2. Electrons jump from the fourth orbit to the second orbit: Here, the electrons are moving from a higher energy level (n = 4) to a lower energy level (n = 2), resulting in a larger energy difference compared to the first case. So, the emitted radiation will have a higher frequency than in the first case.
3. Electrons jump from the first orbit to the second orbit: In this case, the electrons are moving from a lower energy level (n = 1) to a higher energy level (n = 2). Since the initial energy level is lower, the energy difference will be larger, resulting in a higher frequency of the emitted radiation compared to the second case.
4. Electrons jump from the third orbit to the first orbit: In this case, the electrons are moving from a higher energy level (n = 3) to a lower energy level (n = 1). This energy difference is the largest among all the given cases, indicating the highest frequency of emitted radiation.
Therefore, in the given cases, the frequency of emitted radiation is greatest when electrons jump from the third orbit to the first orbit.