Step 1: In single-slit diffraction, the condition for the \( m \)-th diffraction minimum is given by:
\[ a \sin \theta_m = m\lambda, \]
where \( a \) is the width of the slit, \( \lambda \) is the wavelength of light, and \( m \) is the diffraction order.
Step 2: For the 2nd order minimum of \( \lambda_1 \) and the 3rd order minimum of \( \lambda_2 \), we can set the angle for both minima equal since they coincide:
\[ 2\lambda_1 = 3\lambda_2 \]
Thus:
\[ \frac{\lambda_1}{\lambda_2} = \frac{3}{2}. \]
\( \text{M} \xrightarrow{\text{CH}_3\text{MgBr}} \text{N} + \text{CH}_4 \uparrow \xrightarrow{\text{H}^+} \text{CH}_3\text{COCH}_2\text{COCH}_3 \)
Identify the ion having 4f\(^6\) electronic configuration.