A particular hydrogen like ion emits radiation of frequency 2 . 92...

As we know,

$ν ∝ \left[1{n}_{1}^{2} - 1{n}_{2}^{2}\right]$

$\dfrac{2.92 \times {10}^{15}}{ν} = \dfrac{\left[\dfrac{1}{1} - \dfrac{1}{9}\right]}{\left[\dfrac{1}{1} - \dfrac{1}{4}\right]}$

$ν = 2.92 \times {10}^{15} \times \dfrac{3}{4} \times \dfrac{9}{8}$

$ν = 2.46 \times {10}^{15}Hz$