Question

Carbon absorbs energy at a wavelength of 150. nm. The total amount of energy emitted by a carbon sample is 1.00 x 10^5 J. Calculate the number of carbon atoms present in the sample, assuming that each atom emits one photon.

Answer 1

Answer -

Given,

Wavelength = 150 nm

Energy Emitted by carbon = 1.00 * 10⁵ J

Assuming each atom emits one photon.

Number of Cabon atoms present in sample = ?

We know that,

1 nm = 10^-9 m

So,

150 nm = 150 * 10^-9 m

150 nm = 1.5 * 10^-7 m ----------------------1

Now,

Energy emitted by photon is,

E = hc/

where,

h = planck's constant (6.626 * 10^-34 J.s)

c = speed of light (3 * 10⁸ ms^-1)

So,

Energy emitted by 1 photon = [(6.626 * 10^-34 J.s)(3 * 10⁸ ms^-1)] / -----------2

Put 1 in 2,

Energy emitted by 1 photon = [(6.626 * 10^-34 J.s)(3 * 10⁸ ms^-1)] / 1.5 * 10^-7 m

Energy emitted by 1 photon = 13.252 * 10^-19 J

Energy emitted by 1 photon = 1.3252 * 10^-18 J

Now,

Assuming each atom emits one photon.

So,

Energy emitted by 1 atom = 1.3252 * 10^-18 J

Now,

Number of atoms = Energy / (Energy emitted by 1 atom)

So,

Number of atoms = 1.00 * 10⁵ J / (1.3252 * 10^-18 J)

Number of atoms = 7.55 * 10²² [ANSWER]