1. In the electrically neutral atoms, determine the following.

(a) How many protons are in the thorium ²³²₉₀Th nucleus?

(b) How many neutrons are in the lead ²⁰⁶₈₂Pb nucleus?

(c) How many electrons are in orbit about the niobium ⁹³₄₁Nb nucleus?

2. (a) Determine the mass defect (in atom mass units) for helium ³₂He, which has an atom mass of 3.016 030 u.

(b) Determine the mass defect (in atom mass units) for the isotope of hydrogen known as tritium ³₁T, which has an atom mass of 3.016 050 u.

(c) On the basis of your answer to parts(a) and (b), state which nucleus requires more energy to disassemble it into separate and stationary constituent nucleons.

- ³₁T

-³₂He

Give your reasoning.

3. (a) Energy is required to separate a nucleus into its constituent nucleons, as the figure below indicates; this energy is the total binding energy of the nucleus.

In a similar way one can speak of the energy that binds a single nucleon to the remainder of the nucleus. For example, separating nitrogen into nitrogen ¹⁴₇N into nitrogen ¹³₇N and a neutron takes energy equal to the binding energy of the neutron, as shown below:

¹⁴₇N + Energy → ¹³₇N + ¹₀n

Find the energy (in MeV) that binds the neutron to the ¹⁴₇N nucleus by considering the mass of ¹³₇N (atomic mass = 13.005 738 u) and the mass of ⁰₁n (atomic mass = 1.008 665 u), as compared to the mass of ¹⁴₇N (atomic mass = 14.003 .74 u).

(b) Similarly, one can speak of the energy that binds a single proton to ¹⁴₇N nucleus:

Following the procedure outlined in part (a), determine the energy (in MeV) that binds the proton (mass atomic = 1.007825 u) to the ¹⁴₇N nucleus. The atomic mass of carbon ¹³₆C is 13.003 355 u.

(c) Which nucleon is more tightly bound, the neutron or the proton?

-neutron

-proton

4. Write the β^- decay process for carbon ¹⁴₆C, including the chemical symbols as well as the values of Z and A for the parent and daughter nuclei and the β^- particle.

- ¹⁴₆C → ¹⁴₇N + ⁰₊₁e

- ¹⁴₆C → ¹⁴₅B + ⁰_-1e

- ¹⁴₆C → ¹⁴₇N + ⁰_-1e

- ¹⁴₆C → ¹⁴₅B + ⁰₊₁e

5. In the form ^A_ZX, identify the daughter nucleus that results when the following occur.

(a) Curium ²⁴²₉₆Cm undergoes α decay.

(b) Sodium ²⁴₁₁Na undergoes β^- decay.

(c) Nitrogen ¹³₇N undergoes β⁺ decay.

6. Radon ²²⁰₈₆Rn produces a daughter nucleus that is radioactive. The daughter, in turn, produces its own radioactive daughter, and so on. This process continues until lead ²⁰⁸₈₂Pb is reached. What are the total number N_α of α particles and the total number N_β of β^- particles that are generated in this series of radioactive decays?

7. Two pure tones are sounded together. The drawing shows the pressure variations of the two sound waves, measured with respect to atmospheric pressure, where t₁ = 0.0202 s and t₂ = 0.0240 s. What is the beat frequency?

8. In a Young's double-slit experiment, the wavelength of the light used is 505 nm (in vacuum), and the separation between the slits is 2.20 x 10^-6 m. Determine the angle that locates each of the following.

(a) the dark fringe for which m = 0

(b) the bright fringe for which m = 1

(c) the dark fringe for which m = 1

(d) the bright fringe for which m = 2

9. The dark fringe for m = 0 in a Young's double slit experiment is located at an angle of θ = 19^o. What is the angle that locates the dark fringe for m = 1?

10. In a Young's double-slit experiment, the seventh dark fringe is located 0.027 m to the side of the central fringe on a flat screen, which 1.1 m away from the sites. The separation between the slits is 1.30 x 10^-4 m. What is the wavelength of the light being used?

11. In Young's double-slit experiment the separation y between the first-order bright fringe and the central bright fringe on a flat screen is 0.0220 m when the light has a wavelength of 465 nm. Assume that the angles that locate the fringes On the Screen are small enough so that sin θ = tan θ. Find the separation y when the light has a wavelength of 611 nm.