Question

The objective lens of a telescope has a focal length 25 cm and is being used to look at a 50 m-high tree 1 kilometer away. What is the height of the image formed by this telescope lens inside the tube of the telescope? (In mm, closest answer.)

AND

A radioactive sample has a certain number N of unstable nuclei that are emitting 4.5 MeV gamma rays with a half-life of 1.5 hours. If the rate of radioactive heating of the sample due to these decays is 13 watts, how many unstable nuclei are initially in the sample?

AND

A muon at rest decays into an electron, an anti-electron neutrino, and a muon neutrino. After the decay, the electron has a total energy of 52.85 MeV and the anti-electron neutrino has an energy of 20 MeV. What is the energy of the muon neutrino (in MeV, closest answer)?

AND

*Suppose that a particle of mass m is confined to a region of width a. Its energy in the ground state must be of order (the particle is non-relativistic)– (1) $\bar{h}$ ^2/(ma^2 ). (2) 2 eV. (3) $\bar{h}$ /a. (4) $\bar{h}$ ^2 *am. (5) $\bar{h}$ ^2/(ma).

*(don't truly comprehend this last one specially-thanks.)

Answer 1

(i) What is the height of an image formed by this telescope lens inside the tube of the telescope?

Using a formula, we have

m = d_i / d₀ $\Leftrightarrow$ (h_i / h₀) = (f₀ / d₀)

h_i = h₀ (f₀ / d₀)

h_i = [(50 m) (0.25 m)] / (1000)

h_i = 0.0125 m

Converting 'm' into 'mm' :

h_i = 12.5 mm