Question

If \(\lambda_{\gamma} \lambda_{\mathrm{x}}\) and \(\lambda_{\mathrm{m}}\) are the wave lengths of the \(\gamma\) -rays, \(\mathrm{x}\) rays and micro waves respectively in space then (A) \(\lambda_{\gamma}>\lambda_{\mathrm{x}}>\lambda_{\mathrm{m}}\) (B) \(\lambda_{\gamma}<\lambda_{\mathrm{x}}<\lambda_{\mathrm{m}}\) (C) \(\lambda_{r}=\lambda_{x}=\lambda_{m}\) (D) \(\lambda_{\gamma}<\lambda_{\mathrm{m}}<\lambda_{\mathrm{x}}\)

Short answer

The correct answer is (B) \(\lambda_{\gamma}<\lambda_{\mathrm{x}}<\lambda_{\mathrm{m}}\), as gamma-rays have the shortest wavelengths, x-rays have the next shortest wavelengths, and microwaves have the longest wavelengths.

Step-by-step solution

Identify the wavelengths of gamma-rays, x-rays, and microwaves

Gamma-rays have the shortest wavelengths among these three types of radiation, which is typically less than 0.1 nm. X-rays have the next shortest wavelengths typically between 0.1 nm and 100 nm. Microwaves have the longest wavelengths typically between 1 mm and 100 cm.

Compare the wavelengths

Based on the identified wavelengths: - Gamma-rays (\(\lambda_{\gamma}\)) have the shortest wavelengths. - X-rays (\(\lambda_{\mathrm{x}}\)) have the next shortest wavelengths. - Microwaves (\(\lambda_{\mathrm{m}}\)) have the longest wavelengths. Thus, we can state that \(\lambda_{\gamma}<\lambda_{\mathrm{x}}<\lambda_{\mathrm{m}}\).

Choose the correct answer

Comparing the given options with our conclusion from Step 2, we find that option (B) matches our result: (B) \(\lambda_{\gamma}<\lambda_{\mathrm{x}}<\lambda_{\mathrm{m}}\) So, the correct answer is (B).