The energy levels of a hypothetical atom are shown in the given figure. Let _X , _Y , and _Z be the wavelengths of the photons emitted during the transitions X , Y , and Z respectively. Which of the following mathematical relations is correct?

Step-by-step solution

The energy of a photon emitted during a transition is given by E = hc . For transition X (from -E to -3E ): E_X = -E - (-3E) = 2E hc _X = 2E _X = hc 2E For transition Y (from -3E to -7E ): E_Y = -3E - (-7E) = 4E hc _Y = 4E _Y = hc 4E For transition Z (from -E to -7E ): E_Z = -E - (-7E) = 6E hc _Z = 6E _Z = hc 6E Comparing _X and _Y : _X _Y = hc 2E hc 4E = 4E 2E = 2 _X = 2 _Y Answer: _X = 2 _Y