Explanation

Explanation

Explanation

Explanation

Explanation

To find the work function, we need to calculate the energy of the photon (E) and the kinetic energy of the electron (KE), then use the equation:

φ = E - KE

E = hc / λ = 1240 eV nm / 4000 nm = 3.1 eV

KE = (1/2)mv^2 ≈ (1/2) × 9.11 × 10^-31 kg × (6 × 10^5 m/s)^2 ≈ 1.64 × 10^-19 J ≈ 1.024 eV

φ = 3.1 eV - 1.024 eV ≈ 2.076 eV ≈ 2.1 eV

Explanation

Given:

Energy of photon (E) = 4.1 MeV

The total energy available for the electron and positron is:

E - 2 × 0.511 MeV = 4.1 MeV - 1.022 MeV = 3.078 MeV

Since the electron and positron share the energy equally, the kinetic energy of the electron is:

3.078 MeV / 2 = 1.539 MeV

Adding the rest mass energy of the electron (0.511 MeV), we get:

Energy of electron = 1.539 MeV + 0.511 MeV = 2.05 MeV

Explanation

Initial efficiency (η) = 40% = 0.4

Sink temperature (Tc) = 300 K

Initial source temperature (Th) = 300 / (1 - 0.4) = 500 K

New efficiency (η_new) = 0.4 + 0.5(0.4) = 0.6

New source temperature (Th_new) = 300 / (1 - 0.6) = 750 K

Increase in temperature = Th_new - Th = 750 - 500 = 250 K

Explanation

Explanation

Explanation

Kepler's Third Law of Planetary Motion states:

T² = (4π²/G * (M₁ + M₂)) * a³

Where:

T = Orbital Period

a = Semi-major Axis

G = Gravitational Constant

M₁ and M₂ = Masses of the two bodies (e.g., planet and star)

This law shows that the square of the orbital period (T) is proportional to the cube of the semi-major axis (a).