1. A beta particle with a mass of 9.11 x 10^-31 kg is moving at a velocity of 2.5 x 10^7 m/s. Calculate its kinetic energy. 2. An alpha particle with a mass of 6.64 x 10^-27 kg is moving at a velocity of 1.2 x 10^6 m/s. Calculate its momentum. 3. A gamma ray photon has an energy of 2.5 MeV (mega-electron volts). Calculate its wavelength in meters. 4. A radioactive substance has a decay constant of 0.02 s^-1. Calculate its half-life. 5. A beta particle with a charge of -1.6 x 10^-19 C passes through a region of air with a mass of 0.1 kg. Calculate the exposure to ionizing radiation in C/kg. 6. An alpha particle with an energy of 5 MeV is incident on a material. If the stopping power of the material is 2 MeV/cm, calculate the range of the alpha particle in the material. 7. A gamma ray photon with an energy of 1 MeV is absorbed by a material, depositing 2 x 10^-14 J of energy. Calculate the absorbed dose in Gy (gray). 8. A radioactive source has an activity of 5000 Bq (becquerels). If the decay constant is 0.05 s^-1, calculate the number of radioactive atoms present. 9. A beta particle with an energy of 2 MeV is emitted from a radioactive source. If the mass of the beta particle is 9.11 x 10^-31 kg, calculate its velocity. 10. An alpha particle with an energy of 4 MeV is incident on a target material. If the cross-sectional area for interaction is 5 x 10^-15 m^2, calculate the number of alpha particles interacting per second.

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1. The kinetic energy (KE) of a particle can be calculated using the formula KE = 1/2 mv^2, where m is the mass and v is the velocity. Substituting the given values, we get KE = 1/2 * (9.11 x 10^-31 kg) * (2.5 x 10^7 m/s)^2 = 2.84 x 10^-15 Joules.

2. The momentum (p) of a particle can be calculated using the formula p = mv, where m is the mass and v is the velocity. Substituting the given values, we get p = (6.64 x 10^-27 kg) * (1.2 x 10^6 m/s) = 7.97 x 10^-21 kg*m/s.

3. The wavelength (λ) of a photon can be calculated using the formula E = hc/λ, where E is the energy, h is Planck's constant (6.63 x 10^-34 Js), and c is the speed of light (3 x 10^8 m/s). Rearranging for λ, we get λ = hc/E. Substituting the given values, we get λ = (6.63 x 10^-34 Js * 3 x 10^8 m/s) / (2.5 MeV * 1.6 x 10^-13 J/MeV) = 1.98 x 10^-12 m.

4. The half-life (T) of a radioactive substance can be calculated using the formula T = ln(2)/λ, where λ is the decay constant. Substituting the given value, we get T = ln(2) / 0.02 s^-1 = 34.66 seconds.

5. The exposure to ionizing radiation can be calculated using the formula X = Q/m, where Q is the charge and m is the mass. Substituting the given values, we get X = (-1.6 x 10^-19 C) / 0.1 kg = -1.6 x 10^-18 C/kg.

6. The range (R) of a particle in a material can be calculated using the formula R = E/S, where E is the energy and S is the stopping power. Substituting the given values, we get R = (5 MeV) / (2 MeV/cm) = 2.5 cm.

7. The absorbed dose (D) in gray can be calculated using the formula D = E/m, where E is the energy and m is the mass. Substituting the given values, we get D = (2 x 10^-14 J) / (1 kg) = 2 x 10^-14 Gy.

8. The number of radioactive atoms (N) present can be calculated using the formula N = A/λ, where A is the activity and λ is the decay constant. Substituting the given values, we get N = (5000 Bq) / (0.05 s^-1) = 1 x 10^5 atoms.

9. The velocity (v) of a particle can be calculated using the formula E = 1/2 mv^2, where E is the energy and m is the mass. Rearranging for v, we get v = sqrt(2E/m). Substituting the given values, we get v = sqrt((2 MeV * 1.6 x 10^-13 J/MeV) / (9.11 x 10^-31 kg)) = 2.65 x 10^8 m/s.

10. The number of alpha particles interacting per second can be calculated using the formula N = A/σ, where A is the activity and σ is the cross-sectional area. Substituting the given values, we get N = (4 MeV) / (5 x 10^-15 m^2) = 8 x 10^14 particles/s.