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 2.81 ✕ 105 m/s and enter a uniform magnetic field of 0.605 T directed perpendicularly to the velocity of the ions. What is the distance between the impact points formed on the photographic plate by singly charged ions of 235U and 238U?

Answer 1

Answer:

0.2 m

Explanation:

magnetic force = centripetal force

qvB = mv² / r

cancel v on both side and make r subject of the formula

r₁ = mv / qB where m = mass of ion, v = velocity of the ion

r₁  = ( 235 × 1.67 × 10⁻²⁶ × 2.81 × 10⁵) / ( 1.6 × 10⁻¹⁹ × 0.605 T) = 1139.24 × 10⁻² = 11.4 m

r₂ = ( 238 × 1.67 × 10⁻²⁶ × 2.81 × 10⁵) / ( 1.6 × 10⁻¹⁹ × 0.605 T)  = 1153.78 × 10⁻² = 11.5 m

D, distance between the impact points formed = d₂ - d₁ where d₂ and d₁ represent the diameters of the charged ions

D = (2 × 11.5 m) - ( 2 × 11.4) = 2 ( 11.5 - 11.4) = 0.2 m