Vitamin D is produced in the skin when 7-dehydrocholesterol reacts with UVB rays (ultraviolet B) having wavelengths between
270 nm and 300 nm. What is the energy range of the UVB photons?

Respuesta :

UVB photons, with wavelengths between 270 nm and 300 nm, have energies in the range of 6.63 × 10⁻¹⁹ J - 7.37 × 10⁻¹⁹ J.

UVB rays have wavelengths (λ) between 270 nm and 300 nm. We can calculate the energy (E) associated with each wavelength using the Planck-Einstein's relation.

[tex]E = \frac{h \times c}{\lambda }[/tex]

where,

  • h: Planck's constant (6.63 × 10⁻³⁴ J.s)
  • c: speed of light (3.00 × 10⁸ m/s)

The energy associated with a wavelength of 270 nm is:

[tex]E = \frac{h \times c}{\lambda } = \frac{(6.63 \times 10^{-34}J.s ) \times (3.00 \times10^{8}m/s )}{270 \times 10^{-9}m } = 7.37 \times 10^{-19} J[/tex]

The energy associated with a wavelength of 300 nm is:

[tex]E = \frac{h \times c}{\lambda } = \frac{(6.63 \times 10^{-34}J.s ) \times (3.00 \times10^{8}m/s )}{300 \times 10^{-9}m } = 6.63 \times 10^{-19} J[/tex]

UVB photons, with wavelengths between 270 nm and 300 nm, have energies in the range of 6.63 × 10⁻¹⁹ J - 7.37 × 10⁻¹⁹ J.

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