I'm going to answer this the way the equations suggest they should be answered. I'm hoping someone will see it and figure out the error if there is one.
Givens
H1
m1 = 1.67*10^-27
q1 = 1.6 * 10^-19
B = 0.500 T
V = a constant. We don't need the exact value.
R1 = ??
H2
m2 = 3.34 * 10^27
q2 = 1.6 * 10^-19
B = 0.500
R2 = 55.6 cm = 55.6 cm [ 1 m/100 cm ] = 0.556 m
v = a constant. We don't need to know it. It's a constant and it will cancel.
Formula
qvB = m v^/R Cancel one v on each side.
qB = mv/R
Four Tier Formula
Solve for R
RqB = m*v
R = mv/qB
Solution
The four tier fraction looks like the result given below.
[tex]\dfrac{R_1}{R_2} = \dfrac{\dfrac{m_1*v}{q*B}}{\dfrac{m_2*v}{qB}}[/tex]
You can invert the the bottom fraction, but you should be able to see that the "v, q, B" values are the same for all constants. So they cancel. Allthatis left is
[tex]\dfrac{R_1}{R_2}=\dfrac{m_1}{m_2}[/tex]
R2 is given
m2 is 2 times m1 so the fraction m1/m2 = 1/2
R2 = 55.6 cm = 0.556 m
R1/0.556= 1/2 Multiply both sides by 0.556
R1 = 1/2 * 0.556
R1 = 0.278 m which they have left in cm. which is just fine. Anyway the formula gives D [55.6 cm] and that's what you have to go with. But my instincts tell me this isn't right.
Five
A is wrong. They wouldn't be isotopes if they had the same mass.
B is Correct. An Isotope is an atom. They must remain that way or else we have not been given good information. If you have to supply just one answer pick D, but this is a bad question.
C no they different neutrons. That's how isotopes are defined.
D is also correct. If they are a beam, they must have the same velocity.
