A particular hydrogen-like ion emits radiation of frequency2.467 × 1015 Hz when it makes transition from n = 2 to n = 1.What will be the frequency of the radiation emitted a transitionfrom n = 3 to n = 1?
Question
A particular hydrogen-like ion emits radiation of frequency2.467 × 1015 Hz when it makes transition from n = 2 to n = 1.What will be the frequency of the radiation emitted a transitionfrom n = 3 to n = 1?
Solution
To find the frequency of the radiation emitted during the transition from n = 3 to n = 1, we can use the formula for the frequency of radiation emitted by a hydrogen-like ion:
f = R * (Z^2 / n^2) * (1 / n_initial^2 - 1 / n_final^2)
Where:
- f is the frequency of the radiation emitted
- R is the Rydberg constant (approximately 3.29 × 10^15 Hz)
- Z is the atomic number of the ion (in this case, it is not specified)
- n_initial is the initial energy level (n = 3)
- n_final is the final energy level (n = 1)
Substituting the given values into the formula, we have:
f = R * (Z^2 / 3^2) * (1 / 3^2 - 1 / 1^2)
Simplifying the equation:
f = R * (Z^2 / 9) * (1/9 - 1)
f = R * (Z^2 / 9) * (-8/9)
f = -8R * (Z^2 / 81)
Since the atomic number (Z) is not specified, we cannot determine the exact frequency of the radiation emitted during the transition from n = 3 to n = 1.
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