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Zorluk: OrtaNatural Radioactivity and Radiation Emissions

A narrow beam containing α\alpha-particles, β−\beta^--particles, and γ\gamma-rays enters a region of uniform magnetic field acting perpendicularly into the plane of the paper. If all three emissions enter with the same speed, which of the following observations correctly describes their paths in the magnetic field?

  1. The β−\beta^--particles curve more sharply than the α\alpha-particles and in the opposite direction, while γ\gamma-rays continue straight without deflection.Cevap
  2. B
    The α\alpha-particles curve more sharply than the β−\beta^--particles in the opposite direction, while γ\gamma-rays are deflected parallel to the magnetic field.
  3. C
    Both α\alpha-particles and β−\beta^--particles curve in the same direction, but the α\alpha-particles undergo a larger deflection due to their +2e+2e charge.
  4. D
    The γ\gamma-rays curve towards the negative region while α\alpha-particles and β−\beta^--particles travel straight through without deflection.

Cevap

The beta-minus particles curve more sharply than the alpha particles and in the opposite direction, while gamma rays continue straight without deflection.
The magnetic force on a moving charged particle supplies the necessary centripetal force (qvB=mv2rqvB = \frac{mv^2}{r}), yielding a radius of curvature of r=mvqBr = \frac{mv}{qB}. Because a beta-minus particle has an extremely small mass compared to an alpha particle, its mass-to-charge ratio is much lower, resulting in a much tighter (sharper) circular arc. Because alpha particles are positively charged and beta-minus particles are negatively charged, they experience forces in opposite directions. Gamma rays have no charge and are therefore unaffected by the magnetic field.

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1
Identify the charge and mass characteristics of each emission type
Alpha particles (α\alpha) have charge +2e+2e and large mass (≈4 u\approx 4\text{ u}). Beta-minus particles (β−\beta^-) have charge −1e-1e and extremely small mass (≈0.00055 u\approx 0.00055\text{ u}). Gamma rays (γ\gamma) carry zero charge and zero rest mass.
Magnetic forces depend on moving charge (F=qvBF = qvB), while inertia against trajectory changes depends on mass.
2
Determine deflection directions for each emission
Alpha particles (positive) and beta-minus particles (negative) deflect in opposite directions. Gamma rays (neutral) experience zero magnetic force and travel in a straight line.
Particles with opposite sign charges experience magnetic Lorentz forces in opposite directions.
3
Compare curvature extent using the magnetic radius formula r=mvqBr = \frac{mv}{qB}
The mass-to-charge ratio mq\frac{m}{q} for β−\beta^- is far smaller than that for α\alpha. Consequently, rβ≪rαr_{\beta} \ll r_{\alpha}, meaning the β−\beta^- trajectory forms a tighter, sharper curve.
A smaller radius of curvature corresponds to a sharper trajectory deflection in the magnetic field.

Anahtar Kavram

Deflection and Curvature of Radioactive Radiation in Magnetic Fields
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Konular

Natural Radioactivity and Radiation Emissions

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