Use R_H = 1.097x10^7 m^-1. Find the wavelength of the n=2-> n=1 line of He+ in nm (one decimal).

JEE Main levelNumerical answerDifficulty 2 of 3as085

Use $R_{H} = 1.097 \times 1 0^{7} m^{- 1}$ . Find the wavelength of the $n = 2 \to n = 1$ line of $He X^{+}$ in nm (one decimal).

Numerical answer type, answer in nm, tolerance 0.1.

For a hydrogen-like ion

1/ λ = Z^{2} R_{H} (1/ n_{f}^{2} - 1/ n_{i}^{2}) = 4 R_{H} (3/4) = 3 R_{H}

. So

λ = 1/ (3 R_{H}) = 30.4 nm