When an electron jumps from nth orbit to orbit, in an imaginary atom obeying Bohr's model, it emit t — Atomic Structure Chemistry Question
Question
When an electron jumps from nth orbit to $1^{st}$ orbit, in an imaginary atom obeying Bohr's model, it emit two radiations of wavelengths 400 nm and 300 nm. The frequency of radiation emitted out in the transition $n = n$ to $n = 1$ will be
💡 Solution & Explanation
The total energy of a single transition equals the sum of energies of intermediate transitions: $E = E_1 + E_2 = \frac{hc}{\lambda_1} + \frac{hc}{\lambda_2}$. The frequency $\nu = \frac{E}{h} = \frac{c}{\lambda_1} + \frac{c}{\lambda_2} = c \left(\frac{1}{\lambda_1} + \frac{1}{\lambda_2}\right) = 3 \times 10^8 \times \left(\frac{1}{400 \times 10^{-9}} + \frac{1}{300 \times 10^{-9}}\right) = 3 \times 10^{17} \left(\frac{1}{400} + \frac{1}{300}\right) = 3 \times 10^{17} \left(\frac{7}{1200}\right) = \frac{21}{12} \times 10^{15} = 1.75 \times 10^{15}$ Hz. Therefore, correct answer is D.