... A mass spectrometer is used to examine the isotopes of uranium. Ions in the

Question

...

A mass spectrometer is used to examine the isotopes of uranium. Ions in the beam emerge from the velocity selector at a speed of 4.03 times 105 m/s and enter a uniform magnetic field of 0.646 T directed perpendicularly to the velocity of the ions. The charge on an electron is 1.602 times 10-19 C. and the atomic mass unit is 1.66 times 10-27 kg What is the distance between the impact point formed on the photographic plate by singly changed ions of 235 U and 238 U ? What is the maximum torque on a 500-turn circular coil of radius 0.55 cm that carries a current of 1.4 m A and resides in a uniform magnetic field of 0.15 t? Answer in units of N.m

Explanation / Answer

U-235: mass = 235.0439 * 1.66 x 10-27 = 3.90 * 10-25 kg
U-238: mass= 238.0508 * 1.66 x 10-27 = 3.95 * 10-25 kg
U-235: r = m v / q B = 3.90 * 10-25 * 4.03 * 10^5 / 1.60 x10-19 * 0.646 = 1.52 m
U-238: r = m v / q B = 3.95 * 10-25 * 4.03 * 10^5 / 1.60 x10-19 * 0.646 = 1.54 m
U-235: d = 2 * 1.52 = 3.04
U-238: d = 2 * 1.54 = 3.08
difference = 3.08 - 3.04 = 0.04 m
= 4.00 cm
-----------------------------------------------------------------
N = 500, r = 0.55 cm, i = 1.4 *10-3 A, B = 0.15 T
Area of the coil is A = pi r^2 = pi ( 0.55 cm)^2 = 0.95 * 10-4 m2
Torque? = N i A B sin 90
= 500 * 1.4 *10-3 A * 0.95 * 10-4 * 0.15 T
= 0.997 *10-6 N m
U-238: r = m v / q B = 3.95 * 10-25 * 4.03 * 10^5 / 1.60 x10-19 * 0.646 = 1.54 m
U-235: d = 2 * 1.52 = 3.04
U-238: d = 2 * 1.54 = 3.08
difference = 3.08 - 3.04 = 0.04 m
= 4.00 cm
-----------------------------------------------------------------
N = 500, r = 0.55 cm, i = 1.4 *10-3 A, B = 0.15 T
Area of the coil is A = pi r^2 = pi ( 0.55 cm)^2 = 0.95 * 10-4 m2
Torque? = N i A B sin 90
= 500 * 1.4 *10-3 A * 0.95 * 10-4 * 0.15 T
= 0.997 *10-6 N m N = 500, r = 0.55 cm, i = 1.4 *10-3 A, B = 0.15 T
Area of the coil is A = pi r^2 = pi ( 0.55 cm)^2 = 0.95 * 10-4 m2
Torque? = N i A B sin 90
= 500 * 1.4 *10-3 A * 0.95 * 10-4 * 0.15 T
= 0.997 *10-6 N m

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