Explanation

Explanation

Explanation

Bohr's quantum condition states that the angular momentum of an electron in a circular orbit is quantized:

mvr = nh / 2π

where m is the mass of the electron,

v is the velocity,

r is the radius of the orbit,

n is the principal quantum number,

and h is Planck's constant.

Explanation

Explanation

Explanation

Explanation

Using Wien's displacement law:

λ_peak ∝ 1/T

Given: Initial temperature (T1) = 6000 K, Initial peak wavelength (λ1) = 4800 Å

Final temperature (T2) = 3000 K

λ2 / λ1 = T1 / T2

λ2 = λ1 * T1 / T2

= 4800 Å * 6000 K / 3000 K

= 9600 Å

Explanation

According to the law of universal gravitation:

F ∝ (m1 × m2) / r^2

Initially, F0 ∝ (m × m) / r^2

After doubling the mass and halving the distance:

F_new ∝ (2m × 2m) / (r/2)^2

= 16 × F0

Explanation

The Fermi energy is the highest energy level that electrons occupy at absolute zero temperature.

Above this energy, states are empty, and below it, they are filled.

Explanation

Total mechanical energy (E) = (1/2) × m × ω^2 × A^2

ω = 2π / T = 2π / 0.20 s = 10π rad/s

m = 40 g = 0.04 kg

A = 2.0 cm = 0.02 m

E = (1/2) × 0.04 kg × (10π rad/s)^2 × (0.02 m)^2

= 8.0 × 10^-3 J