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Chapter 6: Q2E (page 1275)

Question: The human eye is most sensitive to green light of wavelength 505 nm. Experiments have found that when people are kept in a dark room until their eyes adapt to the darkness, a singlephoton of green light will trigger receptor cells in the rods of the retina. (a) What is the frequency of this photon? (b) How much energy (in joules and electron volts) does it deliver to the receptor cells? (c) To appreciate what a small amount of energy this is, calculate how fast a typical bacterium of mass 9.5 x 10-12 g would move if it had that much energy.

Short Answer

Expert verified

The photon鈥檚 frequency, energy and velocity are 5.94脳1014鈥�Hz,2.46鈥�eV,9.1鈥�mm/srespectively.

Step by step solution

01

(a) Determination of the frequency of the photon.

The frequency of a photon is,

f=c位

Substitute c=3脳108鈥�m/s鈥�and鈥�位=505脳10-9鈥�m

f=3脳108m/s505脳10-9m=5.94脳1014m

02

(b) Determination of energy delivered to receptor cells.

The energy of a photon is,

E = hf

Substituteh=6.626脳10-34J鈰�s鈥�and鈥�f=5.94脳1014鈥�Hz

E=6.626脳10-34J路s5.94脳1014Hz=3.04脳10-19J=2.46eV

03

(b) Determination of the velocity of the bacterium. 

The kinetic energy of the photon is,

K=12mv2

Solve for the velocity,

v=2Km

Substitute all the values in above equation,

v=23.94脳10-19J9.5脳10-15kg=9.1mm/s

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Most popular questions from this chapter

Question:The hydrogen iodide (\(HI\)) molecule has equilibrium separation\(0.16nm\)and vibrational frequency\(6.93 \times {10^{13}}Hz\). The mass of a hydrogen atom is\(1.67 \times {10^{ - 27}}kg\), and the mass of an iodine atom is\(2.11 \times {10^{ - 25}}kg\). (a) Calculate the moment of inertia of\(HI\)about a perpendicular axis through its centre of mass. (b) Calculate the wavelength of the photon emitted in each of the following vibration rotation transitions:

  1. \(n = 1,l = 1 \to n = 0,l = 0\);
  2. \(n = 1,l = 2 \to n = 0,l = 1\);
  3. \(n = 2,l = 2 \to n = 1,l = 3\).

A CD-ROM is used instead of a crystal in an electron diffraction experiment. The surface of the CD-ROM has tracks of tiny pits with a uniform spacing of 1.60渭m. (a) If the speed of the electrons is1.26脳104m/s , at which values of胃 will the m = 1 and m = 2 intensity maxima appear? (b) The scattered electrons in these maxima strike at normal incidence a piece of photographic film that is 50.0 cm from the CD-ROM. What is the spacing on the film between these maxima?

How fast must a rocket travel relative to the earth so that time in the rocket 鈥渟lows down鈥� to half its rate as measured by earth-based observers? Do present-day jet planes approach such speeds?

CP A beam of electrons is accelerated from rest and then passes through a pair of identical thin slits that are 1.25 nm

apart. You observe that the first double-slit interference dark fringe occurs at 18.0 from the original direction of the beam

when viewed on a distant screen. (a) Are these electrons relativistic? How do you know? (b) Through what potential difference were the electrons accelerated?

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