Points I, II and III in the following plot respectively correspond to ( $\mathrm{V}_{\mathrm{mp}}$ : most probable velocity)

(D) $\mathrm{V}_{\mathrm{mp}}$ of $\mathrm{N}_{2}(300 \mathrm{~K})$ ; $\mathrm{V}_{\mathrm{mp}}$ of $\mathrm{O}_{2}(400 \mathrm{~K})$ ; $\mathrm{V}_{\mathrm{mp}}$ of $\mathrm{H}_{2}(300 \mathrm{~K})$

(A) $\mathrm{V}_{\mathrm{mp}}$ of $\mathrm{N}_{2}(300 \mathrm{~K})$ ; $\mathrm{V}_{\mathrm{mp}}$ of $\mathrm{H}_{2}(300 \mathrm{~K})$ ; $\mathrm{V}_{\mathrm{mp}}$ of $\mathrm{O}_{2}(400 \mathrm{~K})$

(B) $\mathrm{V}_{\mathrm{mp}}$ of $\mathrm{H}_{2}(300 \mathrm{~K})$ ; $\mathrm{V}_{\mathrm{mp}}$ of $\mathrm{N}_{2}(300 \mathrm{~K})$ ; $\mathrm{V}_{\mathrm{mp}}$ of $\mathrm{O}_{2}(400 \mathrm{~K})$

(C) $\mathrm{V}_{\mathrm{mp}}$ of $\mathrm{O}_{2}(400 \mathrm{~K})$ ; $\mathrm{V}_{\mathrm{mp}}$ of $\mathrm{N}_{2}(300 \mathrm{~K})$ ; $\mathrm{V}_{\mathrm{mp}}$ of $\mathrm{H}_{2}(300 \mathrm{~K})$

JEE Main · 2019 · 10 Apr 2019 · Shift 2 · States of Matter

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Points I, II and III in the following plot respectively correspond to (

V_{mp}

: most probable velocity)

(A) $V_{mp}$ of $N_{2} (300 K)$ ; $V_{mp}$ of $H_{2} (300 K)$ ; $V_{mp}$ of $O_{2} (400 K)$
(B) $V_{mp}$ of $H_{2} (300 K)$ ; $V_{mp}$ of $N_{2} (300 K)$ ; $V_{mp}$ of $O_{2} (400 K)$
(C) $V_{mp}$ of $O_{2} (400 K)$ ; $V_{mp}$ of $N_{2} (300 K)$ ; $V_{mp}$ of $H_{2} (300 K)$
(D) $V_{mp}$ of $N_{2} (300 K)$ ; $V_{mp}$ of $O_{2} (400 K)$ ; $V_{mp}$ of $H_{2} (300 K)$ ✓ Correct

Answer: (D)

Solution

The most probable speed is

V_{mp} = \frac{2 R T}{M}

, so it scales as

T / M

. For nitrogen at

300 K

this is

300/28 \approx 3.3

, for oxygen at

400 K

it is

400/32 \approx 3.5

, and for the very light hydrogen at

300 K

it is

300/2 \approx 12.3

. Reading the plot from the slowest peak to the fastest, the three points belong to

N X_{2}

300 K

, then

O X_{2}

400 K

, then

H X_{2}

300 K

JEE Main · 2019 · 10 Apr 2019 · Shift 2 · Single correct option

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JEE Main · 2019 · 10 Apr 2019 · Shift 2 · States of Matter

Solution

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