Read the following:
(A) The width of the central band in a diffraction pattern.
(B) The width of the first bright band in the diffraction pattern.
(C) The width of the central band in the diffraction pattern if D is doubled.
(D) The width of the first bright band in the diffraction pattern if D is tripled.
Choose the correct answer from the options given below in increasing order of width.

Question

Mass numbers of two nuclei are in the ratio of 4:3. Their nuclear densities will be in the ratio of:

Answer 1

The width of any band in single-slit diffraction is calculated as:

\[ w = \frac{λD}{d} \]

where:
λ = wavelength of light
D = distance from slit to screen
d = slit width

Band Width Calculations:

A. Original central band width: \( w_A = \frac{2λD}{d} \) (This band is twice the width of other bands).

B. Original first bright band width: \( w_B = \frac{λD}{d} \)

C. Central band width with doubled screen distance: \( w_C = \frac{2λ(2D)}{d} = \frac{4λD}{d} \)

D. First bright band width with tripled screen distance: \( w_D = \frac{λ(3D)}{d} = \frac{3λD}{d} \)

Width Comparisons:

1. Original first bright band (B): \( \frac{λD}{d} \)

2. Original central band (A): \( \frac{2λD}{d} \)

3. First bright band with tripled D (D): \( \frac{3λD}{d} \)

4. Central band with doubled D (C): \( \frac{4λD}{d} \)

Order of Increasing Width: B < A < D < C

The Correct Option is D