Question

10) Covalent bonds in a molecule absorb radiation in the IR region and vibrate at characteristic frequencies.

(a) A molecular vibration absorbs radiation of wavelength 179 μm. What frequency (in s−1) corresponds to that wavelength? Enter your answer in scientific notation. × 10 s−1

(b) A molecular vibration has a frequency of vibration of 7.757 × 1014 Hz. What wavelength (in μm) corresponds to that frequency?

Thank you!!

Answer 1

(a) Given , = 179 m = 179 x 10^-6 m

We have the relation, Frequency, = c /

= 3 x 10⁸ ms^-1 / 179 x 10^-6 m

= (3/179 )x 10^8-(-6) = 1.67 x 10^-2 x 10¹⁴ s^-1 = 1.67 x 10¹² s^-1

Therefore, required frequency = 1.67 x 10¹² s^-1

(b) Given, frequency, = 7.757 x 10¹⁴ Hz = 7.757 x 10¹⁴ s^-1 [Hertz(Hz) = s^-1]

we have the relation,

= c /

=> = c /

=> = 3 x 10⁸ ms^-1 / 7.757 x 10¹⁴ s^-1

=> = (3 /7.757 ) x 10^8-14 m

=> = 0.38 x 10^-6 m

=> = 0.38 m ( since1m = 10^-6 m)

Therefore, required wavelength = 0.38 m