(a) A convex lens with a focal length of 15 cm is placed 25 cm from a lighted object. At what distance will an image be formed? Will it be real?
(b) An object is placed 10 cm from a concave mirror. The focal length is 5 cm. Determine the image distance and the magnification of the image.
(c) Light in vacuum is incident on the surface of a glass slab. In the vacuum, the beam makes an angle of 37.8° with the normal to the surface, while in the glass it makes an angle of 28.6° with the normal. what is the index of refraction of the glass?
(d) Using symbols, write equations to represent the following radioactive decay schemes:
(i) Alpha, (ii)Beta plus (iii)Beta minus and (iv)Gamma decay.
(e) The rate at which radioactive nuclides decay is given by: -ጡN/dt = λ N. Using this decay rate, derive the radioactive decay law, N = N₀e⁻ˡᵗ.
(f) A certain mass of ²³⁸U is kept in a container. What fraction of this radioactive material will be left after 3.0 × 10⁹ years? Take λ = 1.54 × 10⁻¹⁰/year.
(g) What is the binding energy per nucleon of the plutonium isotope ²³⁹₉₄Pu in units of MeV? Here are some atomic masses and the neutron mass as well as the relevant conversion units.
²³⁹Pu 239.05216 u
¹H 1.007825 u
n 1.00867 u
1eV = 1.602 × 10⁻¹⁹ J
1u = 1.6605 × 10⁻²⁷ kg
(h) A radioactive isotope of mercury, ¹⁹⁷Hg, decays to gold, ¹⁹⁷Au, with a disintegration constant of 0.0108 h⁻¹.
(i)Calculate the half-life of the ¹⁹⁷Hg. (ii) What fraction of a sample will remains at the end of three half-lives?
(i) A transverse wave is described by the wave function y(x, t) = (0.30 m) sin[2π/4.50 m (x - 18.00 m/s) t]. Find the (i) amplitude, (ii) wavelength, (iii) wave speed and (iv)the frequency of the wave.