Question

About 0.1 eV is required to break a "hydrogen bond" in a protein molecule. Calculate the minimum frequency and maximum wavelength of a photon that can accomplish this.minimum frequencyHzmaximum wavelengthm

Answer 1

Frequency:
`2.41\cdot 10^(13)Hz`, Wavelength:
`1.24\cdot 10^(-5)m`

Step-by-step explanation:

The energy of the photon is equal to the energy required to break the bond, so 0.1 eV.

First of all, we need to convert the energy of the photon from eV to Joule:

`E=0.1 eV \cdot (1.6\cdot 10^(-19)J/eV)=1.6\cdot 10^(-20) J`

The energy of the photon is related to its frequency by:

`E=hf`

where h is the Planck constant and f is the frequency.

Solving for f,

`f=(E)/(h)=(1.6\cdot 10^(-20)J)/(6.63\cdot 10^(-34)Js)=2.41\cdot 10^(13)Hz`

The wavelength instead is given by

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

where c is the speed of light. Substituting,

`\lambda=(3\cdot 10^8 m/s)/(2.41\cdot 10^(13) Hz)=1.24\cdot 10^(-5)m`