Question

The energies \( E_1 \) and \( E_2 \) of two radiations are 25 eV and 50 eV, respectively. The relation between their wavelengths i.e., \( \lambda_1 \) and \( \lambda_2 \), will be:

• A. \( \lambda_1 = \lambda_2 \)
• B. \( \lambda_1 = 2\lambda_2 \)
• C. \( \lambda_1 = 4\lambda_2 \)
• D. \( \lambda_1 = \frac{1}{2} \lambda_2 \)

Hint:

The wavelength of radiation is inversely proportional to its energy. A higher energy corresponds to a shorter wavelength.

Answer 1

The Correct Option is D

Step 1: The energy of a photon is related to its wavelength by the equation: \[ E = \dfrac{hc}{\lambda}, \] where \( h \) is Planck’s constant and \( c \) is the speed of light.
Step 2: Since energy and wavelength are inversely proportional, the relation between the wavelengths is: \[ \lambda_1 = \frac{1}{2} \lambda_2. \]
Final Answer: \[ \boxed{\lambda_1 = \frac{1}{2} \lambda_2} \]