The energies E₁ and E₂ of two radiations are 25 eV and 50 eV respectively. The relation between their waveleng

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:

Accepted Answer

The energy ($E$) of a photon or radiation is inversely proportional to its wavelength ($\lambda$) according to the Planck-Einstein relation:
$$ E = \frac{hc}{\lambda} $$
where $h$ is Planck's constant and $c$ is the speed of light.

Since $hc$ is constant, we can write the ratio:
$$ \frac{E_1}{E_2} = \frac{\lambda_2}{\lambda_1} $$

**Given:**
*   $E_1 = 25 	ext{ eV}$
*   $E_2 = 50 	ext{ eV}$

**Calculation:**
$$ \frac{25}{50} = \frac{\lambda_2}{\lambda_1} $$
$$ \frac{1}{2} = \frac{\lambda_2}{\lambda_1} $$
$$ \lambda_1 = 2\lambda_2 $$

Thus, the wavelength of the first radiation is twice that of the second.

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