Q.52. If shortest wavelength of hydrogen atom in Lyman series is x, then longest wavelength in Balme

Q: What is the correct answer for JEE Main Chemistry Q52?

The correct answer is D. The Rydberg formula is $\frac{1}{\lambda} = RZ^2 (\frac{1}{n_f^2} - \frac{1}{n_i^2})$. For shortest wavelength in Lyman series of hydrogen atom ($Z=1$, $n_f=1$, $n_i=\infty$): $\frac{1}{x} = R(1)^2 (\frac{1}{1^2} - \frac{1}{\infty^2}) = R$. So $x = \frac{1}{R}$. For longest wavelength in Balmer series of He$^+$ ($Z=2$, $n_f=2$, $n_i=3$): $\frac{1}{\lambda_{Balmer}} = R(2)^2 (\frac{1}{2^2} - \frac{

Q: Q.52. If shortest wavelength of hydrogen atom in Lyman series is x, then longest wavelength in Balmer series of He is :

The correct answer is D. The Rydberg formula is $\frac{1}{\lambda} = RZ^2 (\frac{1}{n_f^2} - \frac{1}{n_i^2})$. For shortest wavelength in Lyman series of hydrogen atom ($Z=1$, $n_f=1$, $n_i=\infty$): $\frac{1}{x} = R(1)^2 (\frac{1}{1^2} - \frac{1}{\infty^2}) = R$. So $x = \frac{1}{R}$. For longest wavelength in Balmer series of He$^+$ ($Z=2$, $n_f=2$, $n_i=3$): $\frac{1}{\lambda_{Balmer}} = R(2)^2 (\frac{1}{2^2} - \frac{

Q: What are the options for this JEE Main Chemistry question?

A. $\frac{9x}{5}$ · B. $\frac{36x}{5}$ · C. $\frac{x}{4}$ · D. $\frac{5x}{9}$

Question

Q.52. If shortest wavelength of hydrogen atom in Lyman series is x, then longest wavelength in Balmer series of He is :

FirstInTest · Accepted Answer

The Rydberg formula is $\frac{1}{\lambda} = RZ^2 (\frac{1}{n_f^2} - \frac{1}{n_i^2})$. For shortest wavelength in Lyman series of hydrogen atom ($Z=1$, $n_f=1$, $n_i=\infty$): $\frac{1}{x} = R(1)^2 (\frac{1}{1^2} - \frac{1}{\infty^2}) = R$. So $x = \frac{1}{R}$. For longest wavelength in Balmer series of He$^+$ ($Z=2$, $n_f=2$, $n_i=3$): $\frac{1}{\lambda_{Balmer}} = R(2)^2 (\frac{1}{2^2} - \frac{1}{3^2}) = 4R (\frac{1}{4} - \frac{1}{9}) = 4R (\frac{9-4}{36}) = 4R (\frac{5}{36}) = \frac{5R}{9}$. So $\lambda_{Balmer} = \frac{9}{5R}$. Substitute $R = \frac{1}{x}$: $\lambda_{Balmer} = \frac{9}{5(1/x)} = \frac{9x}{5}$.

Answer

$\frac{9x}{5}$

Answer

$\frac{36x}{5}$

Answer

$\frac{x}{4}$

Answer

$\frac{5x}{9}$

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