Question

Uranium has two isotopes of masses 235 and 238 units. If both are present in uranium hexa fluoride gas, which would have the larger average speed? If atomic mass of fluorine is 19 units. estimate the percentage difference in speeds at any temperature . ​

Answer 1

$\huge{\underline{\tt{Given:-}}}$

•Uranium isotope of mass :- 235

• Uranium isotope of mass:- 238

• Atomic mass of Uranium :- 19 units

$\huge{\underline{\tt{To\:Find:-}}}$

• Which would have the largest speed.

• Percentage difference in speeds.

$\huge{\underline{\tt{Solution:-}}}$

As we know,

At a fixed temperature, average K.E/molecule =

$\: { \boxed{ \tt{\frac{1}{2} mv {}^{2} = constant}}}$

${ \tt{\frac{1}{2}m_{1}v {}^{2} _{1} = \frac{1}{2}m_{2}v {}^{2} _{2 }}} \\ \\{ \tt{ { \cancel{\frac{1}{2} }}m_{1} v {}^{2} _{1} = { \cancel{ \frac{1}{2} }}m_{2}v {}^{2} _{2} }} \\ \\ { \sf{ \frac{v _{1}}{v _{2}} = \sqrt{ \frac{m _{2} }{m _{1} } } }}$

$....{ \sf{clearly \: smaller \: the \: mass \: of \: the \: molecule}} \\ { \sf{larger \: will \: be \: its \: average \: speed}}....$

★For Uranium (235) hexafluoride ,m1 =

${ \bf{235 + 6 \times 19 = 354 \: units}}$

★For Uranium (238) hexafluoride, m2=

${ \bf{238 + 6 \times19 = 352 \: units}}$

•°• U-235 hexafluoride will have larger average speed.

${ \tt{ {\frac{v_{1}}{v_{2} } = \sqrt{\cancel{ \frac{352}{349}}}}}} \\ \\ = { \tt{1.0044}} \\ \\ { \sf{Percentage \: \: difference \: = \frac{(1.0044 - 1)}{1} \times 100}} \\ \\\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\huge{ \underline{\overline{ \bf{\mid{ 0.44\%}\mid}}}}$

Answer 2

Refer to attachment.....

$\huge{\underline{\underline{\mathfrak{Thank you}}}}$