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 frequency
Hz
maximum wavelength
m

Answer 1

Answer:

$2.41\cdot 10^{13}Hz, 1.24\cdot 10^{-5}m$

Explanation:

The energy of the photon must be equal to 0.1 eV, so let's convert this value into Joules first:

$E=0.1 eV \cdot 1.6\cdot 10^{-19} J=1.6\cdot 10^{-20}J$

The energy of the photon is related to its frequency by

$E=hf$

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

$f=\frac{E}{h}=\frac{1.6\cdot 10^{-20}J}{6.63\cdot 10^{-34}Js}=2.41\cdot 10^{13}Hz$

And now we can find the wavelength of the photon, which is given by

$\lambda=\frac{c}{f}$

where c is the speed of light. Substituting,

$\lambda=\frac{3\cdot 10^8 m/s}{2.41\cdot 10^{13} Hz}=1.24\cdot 10^{-5}m$