JEE Advanced 2026 · Paper 2 · Chemistry Q10

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ChemistryNumerical+4Question 46 of 54

$\mathbf X^{a+}$ and $\mathbf Y^{b+}$ are hydrogen-like species. The wavelength of light absorbed during the transition between the states with principal quantum numbers $n=1$ and $n=2$ of $\mathbf X^{a+}$ is $\lambda$ . The wavelength of light absorbed during the transition between the states with principal quantum numbers $n=2$ and $n=4$ of $\mathbf Y^{b+}$ is $9\lambda$ . The lowest possible value of $(\boldsymbol a+\boldsymbol b)$ is ____.

Your answer

Answer and worked solution

Official answer: 3

For a hydrogen-like ion, $\dfrac1\lambda\propto Z^2\left(\dfrac1{n_1^2}-\dfrac1{n_2^2}\right)$ .

X ( $1\to2$ ): $\dfrac1\lambda\propto\dfrac34Z_X^2$ .
Y ( $2\to4$ ): $\dfrac1{9\lambda}\propto\dfrac3{16}Z_Y^2$ .

Dividing,
$9=\frac{\frac34Z_X^2}{\frac3{16}Z_Y^2}=\frac{4Z_X^2}{Z_Y^2}\implies\frac{Z_Y}{Z_X}=\frac23.$

The smallest integers are $Z_X=3$ ( $\ce{Li^2+}$ , $a=2$ ) and $Z_Y=2$ ( $\ce{He+}$ , $b=1$ ). So $a+b=3$ .

Topics:Bohr model Photoelectric effect and spectra

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JEE Advanced 2026 · Paper 2, Chemistry question 10