Evil alien androids were captured while trying to extract elements for a bomb fr

Question

Evil alien androids were captured while trying to extract elements for a bomb from the water (H_2O) in a nuclear reactor. The setup explained below was found in their nasty underground lair. There are 1.6605 times 10^-27 kg/Atomic Mass Unit (AMU). Use physics to determine what specific Element/Isotope they were trying to collect. (justify your answer with equation, numbers, and logic). The mass spectrometer/collector was set up as follows: The accelerating potential V = +643180.0 Volts (injected-ion-beam) to detector distance was D = 0.200m (so, obviously r = 0.100m) A magnetic field of 2.00 T The injected ions are charged as +e (i.e., a single electron has been knocked out of electron shell)

Explanation / Answer

as it passes through accelerator, it will gain speed

m v^2 /2 = q V

v = sqrt(2 q V / m )

now as it follow circular path under the influence of magnetic force,

q v B = m v^2 / r

q r B = m v

q r B = m sqrt(2 q V / m)

q^2 r^2 B^2 = m^2 2 q V / m

2 m V = q r^2 B^2

V = 643180 volts

q = 1.6 x 10^-19 C

B = 2 T

r = 0.100 m

m = 4.975 x 10^-27 kg

n = m / (1.6605 x 10^-27) = 3

so atomic weight of that element is 3 amu.

Ans: (2 , 1) H+

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