Question

There are two important isotopes of uranium: 235U and 238U. These isotopes have different atomic masses and react differently. Only 235U is very useful in nuclear reactors. One of the techniques for separating them (gas diffusion) is based on the different rms speeds of uranium hexafluoride gas, UF6.

Required:
a. The molecular masses for 235U UF6 and 238U UF6 are 349.0 g/mol and 352.0 g/mol, respectively. What is the ratio of their average velocities?
b. At what temperature would their average velocities differ by 1.00 m/s?
c. Do your answers in this problem imply that this technique may be difficult

Answer 1

See explanation

Step-by-step explanation:

a)Given that;

v235/v238 = √3KT/M235/√3KT/M238

v235/v238 =√M238/M235

M238 = 352.0 g/mol

M235 = 349.0 g/mol

v235/v238 = √352.0 g/mol/349.0 g/mol

v235/v238 = 1.004

b) Given that;

v235 = √3KT/M235

v238 = √3KT1/M238

√3KT/M238 - √3KT/M235 = 1

√T √3K/M238 - √3K/M235 = 1

√T = 1/√3K/M238 - √3K/M235

√T = 1/√3 * 8.31/352 * 10^-3 - √3* 8.31/349 * 10^-3

T = 768 K

c) 768 K is the same as 495 °C hence this process is achievable