consider an atom having four distinct neergy levels. if an electron is able to make transitions between, any two levels, how many different frequencies of radiation could the atom emit

6 different frequencies

Explanation:

From energy level 1 to 2 is one frequency, from energy level 1 to 3 is one frequency and From energy level 1 to 4 is one frequency. So, we have a total of 3 frequencies for transition from energy level 1.

From energy level 2 to 3 is one frequency and from energy level 2 to 4 is one frequency. So, we have a total of 2 frequencies for transition from energy level 2.

From energy level 3 to 4 is one frequency.

So we have a total of 3 + 2 + 1 different frequencies = 6 different frequencies.

Note that the reverse process for each step produces the same frequency as the step in consideration.