Elements Of Physical Chemistry
Elements Of Physical Chemistry
7th Edition
ISBN: 9780198727873
Author: ATKINS, P. W. (peter William), De Paula, Julio
Publisher: Oxford University Press
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Chapter 7, Problem 7.3P

(a)

Interpretation Introduction

Interpretation:

The force exerted by the sail for the spacecraft designed to work by photon pressure which sail was completely absorbing fabric of given area 1km2 and directed a red laser beam with λ650nm has to be calculated.

Concept Introduction:

Louis de Broglie in 1923 rationalized that when light shows particle aspects, then particles of matter display properties of waves under definite circumstances.

λ=hmυp = mυHence λ=hp

h is Planck’s constant(6.63×10-34J.s) which relates energy and frequency.

υ is the speed of particle.

m is the mass of particle.

λ is the wavelength.

p is the momentum.

The above equation is called de Broglie relation.

The force exerted is identified by multiplying photon momentum with Avogadro’s number.

(a)

Expert Solution
Check Mark

Explanation of Solution

Given:

Fabric area A =1km2

Wavelength λ =650nm

The force is determined by multiplying the photon momentum with Avogadro’s number. First the momentum is calculated as follows,

pphoton=hλ=6.626×1034J.s650×109m =1.02×1027kgms1 [here,h=Planck'sconstant(6.626×1034J.s)J=kgm2s2]

F=(NAs1)×pphoton=(6.022×1023s1)(1.02×1027kgms1)=6.14×104N

(b)

Interpretation Introduction

Interpretation:

The exerted pressure by given radiation on the sail for the designed spacecraft has to be calculated.

Concept Introduction:

Louis de Broglie in 1923 rationalized that when light shows particle aspects, then particles of matter display properties of waves under definite circumstances.

λ=hmυp = mυHence λ=hp

h is Planck’s constant(6.63×10-34J.s) which relates energy and frequency.

υ is the speed of particle.

m is the mass of particle.

λ is the wavelength.

p is the momentum.

The above equation is called de Broglie relation.

The force exerted is identified by multiplying photon momentum with Avogadro’s number.

Force per unit area is called pressure.

(b)

Expert Solution
Check Mark

Explanation of Solution

Given:

Fabric area A =1km2

Wavelength λ =650nm

The pressure exerted is as follows,

P=FA=6.14×104N1×106m2 =6.14×1010N/m2

(c)

Interpretation Introduction

Interpretation:

The time taken by the craft of mass 1kg to accelerate speed of 1ms-1 has to be calculated.

Concept Introduction:

Louis de Broglie in 1923 rationalized that when light shows particle aspects, then particles of matter display properties of waves under definite circumstances.

λ=hmυp = mυHence λ=hp

h is Planck’s constant(6.63×10-34J.s) which relates energy and frequency.

υ is the speed of particle.

m is the mass of particle.

λ is the wavelength.

p is the momentum.

The above equation is called de Broglie relation.

The force exerted is identified by multiplying photon momentum with Avogadro’s number.

Force per unit area is called pressure.

According to Newton’s second law the force is equal to ma.

F=m a=mvtt=mvFhere,F=forcem=massa=accelerationt=timetakenv=velocity

(c)

Expert Solution
Check Mark

Explanation of Solution

Given:

Fabric area A =1km2

Wavelength λ =650nm

Speed  =1ms1

Hence, velocity is equal to 1ms1

The time taken is as follows,

t=mvF=1kg×1ms16.14×104N=1628.7s=1.6287×103s=0.45h

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