Explanation

Energy of one photon (E) = hc / λ

h = 6.626 × 10^-34 Js

c = 3 × 10^8 m/s

λ = 4961 Å = 4961 × 10^-10 m

E = (6.626 × 10^-34 Js × 3 × 10^8 m/s) / (4961 × 10^-10 m)

= 4.007 × 10^-19 J

Number of photons required to do 1 J of work:

n = 1 J / (4.007 × 10^-19 J)

= 2.4961 × 10^18

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

Explanation

Explanation

Explanation

Explanation

The energy required to excite an electron from the second orbit to the third orbit is:

ΔE = 13.6Z^2(1/4 - 1/9) eV

Given ΔE = 42.7 eV:

42.7 = 13.6Z^2(1/4 - 1/9)

Solving for Z:

Z = 4

Explanation

Explanation

When current flows through an inductance, it builds up gradually due to the back electromotive force (EMF) induced by the changing current.

This results in an exponential growth of the current over time.

Explanation

To find the frequency, we can use the equation:

v_max = A * ω

where v_max = 31.4 cm/s, A = 5 cm

ω = v_max / A

= 31.4 cm/s / 5 cm

= 6.28 rad/s

Now, ω = 2 * π * f

f = ω / (2 * π)

= 6.28 rad/s / (2 * π)

= 1 Hz

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