Question

Electric power is measured in watts (1 W = 1 J/s). About 95% of the power output of an incandescent bulb is converted to heat and 5% to light. If 12% of that light shines on your chemistry textbook, how many photons per second shine on the book from a 62 W bulb? (Assume that the photons have a wavelength of 504 nm). Enter a number in scientific notation (e.g. 1.23e12).

Answer 1

Answer:

9.430 * 10¹⁷ protons per second whill shine on the book from a 62 W bulb

Explanation:

To answer this question, first let's calculate the energy of a single photon with a wavelength (λ) of 504 nm:

E = hc/λ

Where h is Planck's constant (6.626*10⁻³⁴ J·s) and c is the speed of light (3*10⁸ m/s).

E = 6.626*10⁻³⁴ J·s * 3*10⁸ m/s ÷ (504*10⁻⁹m) = 3.944 * 10⁻¹⁹ J.

So now we can make the equivalency for this problem, that

1 proton =  3.944 * 10⁻¹⁹ J

Now we convert watts from J/s to proton/s:

1 $\frac{J}{s}*\frac{1proton}{3.944*10^{-19}J}=2.535*10^{18} \frac{proton}{s}$ = 1 W

Solving the problem, a 62 W bulb converts 5% of its output into light, so:

• 62 * 5/100 = 3.1 W

3.1 watts are equal to [ 2.535*10¹⁸ proton/s * 3.1 ] = 7.858 * 10¹⁸ proton/s

Of those protons per second, 12% will shine on the chemistry textbook, thus:

7.858 * 10¹⁸ proton/s * 12/100 = 9.430 * 10¹⁷ protons/s