A narrow beam of singly charged potassium ions with a kinetic energy of 32 keV enters a region of width 1.00 cm that contains a magnetic field of strength 0.500 T , as shown in the figure. The ions are subsequently collected on a screen located 95.5 cm away from the magnetic field region. Assuming the beam consists of isotopes with atomic weights 39 and 41 , determine the separation between the points where these iso

Step-by-step solution

The radius of the circular path of an ion in the magnetic field is given by R = mv qB = 2mK qB . Since the width of the magnetic field d is much smaller than R , the deflection angle is small. The angle of emergence is = d R . The transverse deflection of the ion inside the magnetic field is y₁ = R(1 - ) R ^2 2 = d^2 2R . After exiting the magnetic field, the ion travels in a straight line for a distance L to the screen. The additional deflection is y₂ = L L = Ld R . The total deflection on the screen is y = y₁ + y