Matter Waves: de Broglie Wavelength question from NEET 2013

Answer: (d)

1. $\lambda = \dfrac{h}{\sqrt{2mK}}$ with $m_n = 1.675 \times 10^{-27}\text{ kg}$.
2. Taking $K \approx kT$: $\sqrt{2m_nk} = \sqrt{2 \times 1.675 \times 10^{-27} \times 1.38 \times 10^{-23}} \approx 2.15 \times 10^{-25}$
3. $\lambda = \dfrac{6.63 \times 10^{-34}}{2.15 \times 10^{-25}\sqrt{T}} \approx \dfrac{3.08 \times 10^{-9}}{\sqrt{T}}\text{ m} = \dfrac{30.8}{\sqrt{T}}\ \mathring{A}$
4. (With $K = \frac{3}{2}kT$ the value is $25.2/\sqrt{T}$ Å, not listed, so the options use $K = kT$.)
5. So the answer is (d) $\frac{30.8}{\sqrt{T}}\ \mathring{A}$.