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Find the decay constant and the mean life time of { }^{55} {Co

Question

Medium

Solving time: 3 mins

Find the decay constant and the mean life time of $^{55} Co$ radionuclide if its activity is known to decrease $4%$ per hour. The decay product is non-radioactive.

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Book:

Physics Galaxy Optics and Modern Physics Vol 4 (Ashish Arora)

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Find the decay constant and the mean life time of

^{55} Co

radionuclide if its activity is known to decrease

4%

per hour. The decay product is non-radioactive.

15 mins ago

Discuss this question LIVE

15 mins ago

Text solutionVerified

If the decay constant (in (hour)

^{- 1}

) is

λ

, then the activity after one hour will decrease by a factor

e^{- λ}

.
Hence,

0.96 = e^{- λ}

λ = 1.11 \times 1 0^{- 5} s^{- 1}

= 0.0408

per hour
The mean life time is

24.5

hour

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Practice questions from Physics Galaxy Optics and Modern Physics Vol 4 (Ashish Arora)

Question 1

Medium

^{32} P

beta-decays to

^{32} S

. Find the sum of the energy of the antineutrino and the kinetic energy of the

β

-particle. Neglect
the recoil of the daughter nucleus. Atomic mass of

^{32} P = 31.974

amu and that of

^{32} S = 31.972 amu

Topic:

Nuclei

Book:

Physics Galaxy Optics and Modern Physics Vol 4 (Ashish Arora)

View solution

Question 2

Hard

A nuclear reactor generates

P = 20 MW

power at efficiency

η = 60%

by nuclear fission of a radio-nuclide whose half life is

T = 2.2

years. If each fission releases energy

E = 200 MeV

, calculate time during which

μ = 10

mole of the radionuclide will be consumed completely. (Avogadro number,

N = 6 \times 1 0^{23}, lo g_{e} 2 = 0.693, 1

year

=

3.15 \times 1 0^{7} s)

Topic:

Nuclei

Book:

Physics Galaxy Optics and Modern Physics Vol 4 (Ashish Arora)

View solution

Question 3

Medium

Some amount of radio active substance (half life

= 10

days) is spread inside a room and consequently the level of radiation becomes 50 times permissible level for normal occupancy of the room. After how many days would the room be safe for occupation.

Topic:

Nuclei

Book:

Physics Galaxy Optics and Modern Physics Vol 4 (Ashish Arora)

View solution

Question 4

Hard

A radionuclide with disintegration constant

λ

is produced in a reactor at a constant rate

α

nuclei per second. During each decay energy

E_{0}

is released.

20%

of this energy is utilized in increasing the temperature of water. Find the increase in temperature of

m

mass of water in time

t

. Specific heat of water is

s

. Assume that there is no loss of energy through water surface.

Topic:

Nuclei

Book:

Physics Galaxy Optics and Modern Physics Vol 4 (Ashish Arora)

View solution

Practice more questions from Nuclei

Question 1

Medium

_{94}^{239} Pu

is undergoing

α

-decay according to the equation

_{94}^{239} Pu \to_{92}^{235} U +_{2}^{4} He

The process is accompanied by an emission of

γ

-rays of wavelength

0.125 \overset{˚}{A}

. Find the speed of the emitted

α

-particle. Given, mass of

_{94}^{239} Pu = 239.052158 amu

, mass of

_{92}^{235} U = 235.043925 amu

, mass of

_{2}^{4} He = 4.002603 amu

and

1 amu = 931 MeV

Topic:

Nuclei

Book:

Physics Galaxy Optics and Modern Physics Vol 4 (Ashish Arora)

View solution

Question 2

Easy

Atoms having the same ...... but different ...... are called isotopes.

Topic:

Nuclei

Exam:

JEE Advanced 1986

View solution

Question 3

Medium

A sample of radioactive material decays simultaneously by two processes

A

and

B

with half lives

\frac{1}{2}

and

\frac{1}{4} hr

respectively. For first half hr it decays with the process

A

, next one hr with the process

B

and for further half an hour with both

A

and

B

. If originally there were

N_{0}

nuclei, find the number of nuclei after 2 hr of such decay :

$\frac{N _{0}}{( 2 ) ^{8}}$
$\frac{N _{0}}{( 2 ) ^{4}}$
$\frac{N _{0}}{( 2 ) ^{6}}$
$\frac{N _{0}}{( 2 ) ^{5}}$

Topic:

Nuclei

Book:

Physics Galaxy Optics and Modern Physics Vol 4 (Ashish Arora)

View 3 solutions

Question 4

Easy

One Becquerel is defined as

1 disintegration per sec
$1 0^{6}$ disintegration per sec
$3.7 \times 1 0^{10}$ disintegration per sec
$1 0^{3}$ disintegration per sec

Topic:

Nuclei

View solution

Practice questions on similar concepts asked by Filo students

Question 1

7. A man can walk uphill at the rate of 2.5 km/hr. and downhill at the rate of 3.25 km/hr. If the total time required to walk a certain distance up the hill and return to the starting position is 4 hours. 36 min What is the distance he walked up the hill?

Topic:

Motivation and Emotion

View solution

Question 2

4 Part D The space around a coordinate system is conventionally divided into four numbered quadrants depending on the signs of the x and y coordinates (Figure 3).Consider the following conditions: Ax>0.y>0 B.x>0y

Topic:

Physics

View solution

Question 3

This property of the materials tells you why a nylon or plastic comb gets electrified on combing dry hair or on rubbing, but a metal article like spoon does not. The charges on metal leak through our body to the ground as both are conductors of electricity.

Topic:

Electrostats

View solution

Question 4

You really just have to answer 7 questions and not do all of the rest of this. Once you have assembled your spectrometer with the instructions in the lecture and above, use it to examine the spectra of three different light sources. Make sure that at least one of them is the sun or moon, but the others can be incandescent lights, compact fluorescent bulbs, LED lights, halogen or xenon bulbs, televisions, computer screens, candles, fireplaces, etc. Then, answer the following questions in a separate document: Describe the differences in appearance among the three spectra. What feature of the light source do the spectra represent? In other words, what is it that you are actually analyzing? Why do you think spectrometers are so valuable for studying celestial objects? Part 2: Estimating the Number of Visible Stars in the Night Sky For this, you will need an empty toilet roll and a clear, dark night. Before you start, jot down the number of stars that you think you can see in the night sky. Aim your toilet roll at a part of the sky well above the horizon to avoid any haze pollution. Hold your roll steady and allow your eyes to get used to the light for a few seconds. Count the number of stars that you can see within through the roll. Do this four more times in other parts of the sky, and average the five counts. The viewing diameter of a toilet roll is about 1/135th of the entire sky, at least for a relatively flat area. Mountains, buildings or large trees will obscure some of the sky. To determine the number of visible stars, multiply your average by 135. Answer the following questions: 4. How similar is this to your original estimation? 5. What percentage of our galaxy do you think that we can see with the naked eye from Earth? Part 3: Solar System Please answer the following questions: 6. Why do you think that the inner planets are relatively close together, but the outer planets are spaced so widely apart? 7. Why do you think that the gaseous planets are gaseous, but the inner planets are not?

Topic:

Physics

View solution

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Question Text	Find the decay constant and the mean life time of $^{55} Co$ radionuclide if its activity is known to decrease $4%$ per hour. The decay product is non-radioactive.
Topic	Nuclei
Subject	Physics
Class	Class 12
Answer Type	Text solution:1
Upvotes	143