A) \[12.42\times {{10}^{-21}}J,928m/s\]
B) \[8.78\times {{10}^{-21}}J,684m/s\]
C) \[6.21\times {{10}^{-21}}J,968m/s\]
D) \[12.42\times {{10}^{-21}}J,684m/s\]
Correct Answer: D
Solution :
[d] The formula for average kinetic energy is \[\overline{\text{K}\text{.E}\text{.}}=\frac{3}{2}kT\text{ }\therefore \frac{{{\left( \overline{\text{K}\text{.E}\text{.}} \right)}_{600K}}}{{{\left( \overline{\text{K}\text{.E}\text{.}} \right)}_{300K}}}=\frac{600}{300}\] \[\Rightarrow {{(\overline{\text{K}\text{.E}\text{.}})}_{600K}}=2\times 6.21\times {{10}^{-21}}J\] \[=\,12.42\,\times {{10}^{-21}}\,J\] Also the formula for r.m.s. velocity is \[{{C}_{rms}}=\sqrt{\frac{3KT}{m}}\therefore \frac{{{\left( {{C}_{rms}} \right)}_{600K}}}{{{\left( {{C}_{rms}} \right)}_{300K}}}=\sqrt{\frac{600}{300}}\] \[\Rightarrow {{({{C}_{rms}})}_{600K}}=\sqrt{2}\times 484=684m/s\]
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