A technique called mass spectrometry is used to segregate different isotopes of an element. In such a setup, hydrogen gas is sent which is ionized by the ion source and we get nuclei of protium (11H), deuterium (21H) and tritium (31H).
A perpendicular magnetic field is used to deviate these in separate beams. Pick the correct option.
A technique called mass spectrometry is used to segregate different isotopes of an element. In such a setup, hydrogen gas is sent which is ionized by the ion source and we get nuclei of protium (11H), deuterium (21H) and tritium (31H).
A perpendicular magnetic field is used to deviate these in separate beams. Pick the correct option.
The correct option is C a - tritium; b - deuterium; c - protium
The three isotopes, once ionized carry an equal amount of charge each: +1e . The magnetic field should result in an equal force on each of the charges, equal to →F=e(→v×→B), where →v is the velocity of the nuclei when they enter the magnetic field →B, and →B⊥→v. This force will cause a centripetal acceleration →a (because it's always perpendicular to →v), which we can write using Newton's second law, as -
→F=m→a=mv2r^r=e(→v×→B)
Which in scalar form looks like -
F=mv2r=evBsin 90∘=evB⇒1r=eBmv⇒r=mveB. (1)
Interesting right? Since v, e, and are constants in this situation, equation (1) means higher the mass, larger the radius of the circular path that a charged particle takes once it enters a magnetic field perpendicularly. Among the three isotopes - 11H, 21H, and 31H−tritium, 31H is the heaviest - why?
Isotopes have same number of protons but different number of neutrons - same Z but different A. The protium nucleus has just one proton (11H), deuterium nucleus has one proton and one neutron (21H), tritium nucleus has one proton plus two neutrons (31H). Comparing masses, naturally, mtritum >mdeuteriummprotium
So when the three different kinds of nuclei enter the perpendicular magnetic field, their radii of curvature will follow rtritium > mdeuteriummprotium, since by equation, the radius of curvature depends just on the mass. Therefore, a - tritium, b - deuterium, and c - protium.
a - tritium; b - deuterium; c - protium
The three isotopes, once ionized carry an equal amount of charge each: +1e . The magnetic field should result in an equal force on each of the charges, equal to →F=e(→v×→B), where →v is the velocity of the nuclei when they enter the magnetic field →B, and →B⊥→v. This force will cause a centripetal acceleration →a (because it's always perpendicular to →v), which we can write using Newton's second law, as -
→F=m→a=mv2r^r=e(→v×→B)
Which in scalar form looks like -
F=mv2r=evBsin 90∘=evB⇒1r=eBmv⇒r=mveB. (1)
Interesting right? Since v, e, and are constants in this situation, equation (1) means higher the mass, larger the radius of the circular path that a charged particle takes once it enters a magnetic field perpendicularly. Among the three isotopes - 11H, 21H, and 31H−tritium, 31H is the heaviest - why?
Isotopes have same number of protons but different number of neutrons - same Z but different A. The protium nucleus has just one proton (11H), deuterium nucleus has one proton and one neutron (21H), tritium nucleus has one proton plus two neutrons (31H). Comparing masses, naturally, mtritum >mdeuteriummprotium
So when the three different kinds of nuclei enter the perpendicular magnetic field, their radii of curvature will follow rtritium > mdeuteriummprotium, since by equation, the radius of curvature depends just on the mass. Therefore, a - tritium, b - deuterium, and c - protium.
