The energies E1 and E2 of two radiations are 25 eV and 50 eV, respectively. The relation between their wavelengths i.e., λ1 and λ2 will be :

Question

The energies E1 and E2 of two radiations are 25 eV and 50 eV, respectively. The relation between their wavelengths i.e., λ1 and λ2 will be : (A) λ1 = λ2 (B) λ1 = 2λ2 (C) λ1 = 4λ2 (D) λ1 = (1/2)λ2

Tardigrade Admin · Accepted Answer

Given E1 = 25 eV E2 = 50 eV E1 = (hc/λ1) E2 = (hc/λ 2) ∴ (E1/E2) = (λ 2/λ 1) ∴ (λ 2/λ 1) = (25/50) = (1/2) λ 1 = 2λ 2

Q. The energies $E_{1}$ and $E_{2}$ of two radiations are $25 e V$ and $50 e V$ , respectively. The relation between their wavelengths i.e., $λ_{1}$ and $λ_{2}$ will be :

$λ_{1} = λ_{2}$

$λ_{1} = 2 λ_{2}$

$λ_{1} = 4 λ_{2}$

$λ_{1} = \frac{1}{2} λ_{2}$

Given $E_{1} = 25 e V$
$E_{2} = 50 e V$
$E_{1} = \frac{h c}{λ _{1}} E_{2} = \frac{h c}{λ _{2}}$
$∴ \frac{E _{1}}{E _{2}} = \frac{λ _{2}}{λ _{1}}$
$∴ \frac{λ _{2}}{λ _{1}} = \frac{25}{50} = \frac{1}{2}$
$λ_{1} = 2 λ_{2}$

Q. The energies E1​ and E2​ of two radiations are 25eV and 50eV, respectively. The relation between their wavelengths i.e., λ1​ and λ2​ will be :

λ1​=λ2​

λ1​=2λ2​

λ1​=4λ2​

λ1​=21​λ2​