Final answer:
The wavelength of the photon emitted during the n+1 to n transition is approximately 5.471 x 10⁻¹⁴ m, and while not directly stated, the mass of the particle in such problems is frequently assumed to be that of an electron (9.109 x 10⁻³¹kg).
Step-by-step explanation:
To calculate the energy of the photon emitted, we subtract the energy of the n+1 level from the n level. In this case, E = E6 - E5 = 74.2 MeV - 51.5 MeV = 22.7 MeV. Next, we convert this energy to joules using the conversion 1 MeV = 1.602 x 10⁻¹³ J, which yields E = 22.7 x 1.602 x 10⁻¹³ J = 3.6354 x 10⁻¹² J.
To find the wavelength of the photon, we use the equation c = λf, where c is the speed of light in a vacuum and f is the frequency of the photon. We first find the frequency through E = hf, where h is Planck's constant (6.626 x 10⁻³⁴ J·s), and this gives us f = E / h = 3.6354 x 10⁻¹² J / 6.626 x 10⁻³⁴ J·s = 5.485 x 10²¹ s⁻¹. Substituting in λ = c / f, the wavelength λ = (3 x 10⁸ m/s) / (5.485 x 10²¹ s⁻¹) = 5.471 x 10⁻¹⁴ m.
The mass of the particle is not directly given in the question. However, it is a common practice in physics to assume the particle in a quantum box as an electron in a model problem unless otherwise specified, because this kind of problem is typically illustrative and doesn't concern itself with other particles.
Assuming an electron, its rest mass is commonly known to be approximately 9.109 x 10⁻³¹ kg.