Question

What is the energy in kJ/mol of radiation with wavelength of
6.61m?

Answer 1

The energy of radiation with a wavelength of 6.61 meters is calculated using the equation E = hc / λ, followed by adjustments for Avogadro's number and conversion to kilojoules per mole (kJ/mol).

The result is approximately 1.806 x 10^-5 kJ/mol.

Step-by-step explanation:

The energy of radiation can be calculated using the equation E = hc / λ, where E is the energy in joules (J), h is Planck's constant (6.626 x 10-34 J·s), c is the speed of light in a vacuum (3.00 x 108 m/s), and λ is the wavelength of the radiation in meters. To find the energy per mole, we must include Avogadro's number (6.022 x 1023 mol-1) and convert joules to kilojoules by dividing by 1,000.

Let's perform the calculations:

1. First, convert the energy to joules using the formula: E = (6.626 x 10-34 J·s) x (3.00 x 108 m/s) / 6.61m
2. Calculate the energy in J/photon and then multiply it by Avogadro's number to get J/mol.
3. Lastly, convert J/mol to kJ/mol by dividing by 1,000.

Now we can plug the values into the equation and calculate:

1. E = (6.626 x 10-34 J·s) x (3.00 x 108 m/s) / 6.61m = 3.00 x 10-26 J/photon
2. E (kJ/mol) = (3.00 x 10-26 J/photon) x (6.022 x 1023 mol-1) = 1.806 x 10-2 J/mol)
3. E (kJ/mol) = 1.806 x 10-2 J/mol / 1,000 = 1.806 x 10-5 kJ/mol

Therefore, the energy of radiation with a wavelength of 6.61 meters is approximately 1.806 x 10-5 kJ/mol.

Answer 2

Step-by-step explanation:

It is known that relation between frequency and wavelength is as follows.

f =
`(c)/(\lambda)`

where, c = speed of light

`\lambda` = wavelength

Hence, first we will calculate the frequency as follows.

f =
`(c)/(\lambda)`

=
`(3 * 10^(8) m/s)/(6.61 m)`

=
`0.453 * 10^(8)` s

Now, the relation between energy and frequency is as follows.

E = hf

where, h = planck's constant =
`6.63 * 10^(-34)` J/s

E =
`6.63 * 10^(-34) J * 0.453 * 10^(8)`

=
`3.00 * 10^(-26) J`

or, =
`3.00 * 10^(-29) kJ`

As one mole contains
`6.022 * 10^(23)` atoms in a substance.

Hence, there are
`3.00 * 10^(-29) kJ * 6.022 * 10^(23)`

=
`18.066 * 10^(-6)` kJ/mol

Thus, we can conclude that radiation with wavelength of 6.61 m emits
`18.066 * 10^(-6)` kJ/mol of energy.