Final answer:
a. The energy of the photon is 4.97 x 10^-19 J and its momentum is 1.66 x 10^-27 kg·m/s. b. The equivalent mass if all the energy of the photon were converted to mass is 5.53 x 10^-36 kg. c. The mass of the microscopic specimen is 7.17 x 10^-15 kg.
Step-by-step explanation:
a. To determine the energy of a photon, we can use the equation:
E = hf
where E is the energy, h is Planck's constant (6.63 x 10^-34 J·s), and f is the frequency of the photon. Plugging in the given frequency, we have:
E = (6.63 x 10^-34 J·s)(7.50 x 10^14 Hz) = 4.97 x 10^-19 J
To determine the momentum of a photon, we can use the equation:
p = hf/c
where p is the momentum, h is Planck's constant, f is the frequency, and c is the speed of light (3.00 x 10^8 m/s). Plugging in the given frequency, we have:
p = (6.63 x 10^-34 J·s)(7.50 x 10^14 Hz)/(3.00 x 10^8 m/s) = 1.66 x 10^-27 kg·m/s
b. To determine the equivalent mass if all the energy of the photon were converted to mass, we can use Einstein's mass-energy equivalence equation:
E = mc^2
solving for mass (m), we have:
m = E/c^2 = (4.97 x 10^-19 J)/(3.00 x 10^8 m/s)^2 = 5.53 x 10^-36 kg
c. To determine the mass of the microscopic specimen, we can rearrange the de Broglie wavelength equation:
λ = h/mv
solving for mass (m), we have:
m = h/(λv) = (6.63 x 10^-34 J·s)/((8.2 x 10^-14 m)(1.1 x 10^5 m/s)) = 7.17 x 10^-15 kg