In an X -ray tube, electrons emitted from a filament (cathode) carrying current I hit a target (anode) at a distance d from the cathode. The target is kept at a potential V higher than the cathode resulting in emission of continuous and characteristic X-rays. If the filament current I is decreased to I 2 , the potential difference V is increased to 2 V , and the separation distance d is reduced to d 2 , then

the cut-off wavelength will reduce to half, and the intensities of all the X-rays will decrease

the cut-off wavelength as well as the wavelengths of the characteristic X-rays will remain the same

the cut-off wavelength will become two times larger, and the intensity of all the X-rays will decrease

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The activity of a sample of radioactive material is $A_{1}$ at time $t_{1}$ and $A_{2}$ at time $t_{2} (t_{2} > t_{1})$ . Its mean life is T. Which of the following is correct?

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Important Questions on Atoms and Nuclei

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Physics Crash Course JEE Advanced>Chapter 20 - Atoms and Nuclei>Exercise 1>Q 40

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 hour 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.

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Physics Crash Course JEE Advanced>Chapter 20 - Atoms and Nuclei>Exercise 1>Q 41

A radioactive element

X

converts into another stable element

Y

. Half life of

X

2 hrs

. Initially only

X

is present. After time

t

, the ratio of atoms of

X

and

Y

is found to be

1 : 4

, then

t

in hours is

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Physics Crash Course JEE Advanced>Chapter 20 - Atoms and Nuclei>Exercise 1>Q 42

Nuclei of radioactive element

A

are produced at rate

t^{2}

at any time

t

. The element

A

has decay constant

λ .

Let

N

be the number of nuclei of element

A

at any time

t .

At time

t = t_{0}, \frac{d N}{d t}

is minimum. Then the number of nuclei of element

A

at time

t = t_{0}

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Physics Crash Course JEE Advanced>Chapter 20 - Atoms and Nuclei>Exercise 1>Q 43

The activity of a radioactive substance decreased to one-third of the original activity number

N_{0}

in a period of

9 yr

. After a further lapse of

9 yr

, its activity will be

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Physics Crash Course JEE Advanced>Chapter 20 - Atoms and Nuclei>Exercise 1>Q 44

Two radioactive nuclei

P

and

Q

in a given sample decay into a stable nucleus

R

. At time

t = 0

, the number of

P

species are

4 N_{0}

and that of

Q

are

N_{0}

. Half-life of

P

(for conversion to

R

) is

1 minute

whereas that of

Q

2 minutes

. Initially, there are no nuclei of

R

present in the sample. When number of nuclei of

P

and

Q

are equal, the number of nuclei of

R

present in the sample would be,

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Physics Crash Course JEE Advanced>Chapter 20 - Atoms and Nuclei>Exercise 1>Q 45

A parent nucleus $X$ undergoes $α -$ decay with a half-life of $75000$ years. The daughter nucleus $Y$ undergoes $β -$ decay with a half-life of $9$ months. In a particular sample, it is found that the rate of emission of $β -$ particles is nearly constant (over several months) at $10^{7} h^{- 1} .$ What will be the number of $α -$ particles emitted in an hour?

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Physics Crash Course JEE Advanced>Chapter 20 - Atoms and Nuclei>Exercise 1>Q 46

A freshly prepared radioactive source of half-life $2 hr$ emits radiation of intensity which is $64$ times the permissible safe level. The minimum time after which it would be possible to work safely with this source is,

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Physics Crash Course JEE Advanced>Chapter 20 - Atoms and Nuclei>Exercise 1>Q 47

Mass spectrometric analysis of potassium and argon atoms in a moon rock sample shows that the ratio of the number of (stable) $^{40} A r$ atoms present to the number of (radioactive) $^{40} K$ atoms is $10.3$ . Assume that all the argon atoms were produced by the decay of potassium atoms, with a half-life of $1 .25 \times 10^{9} yr$ . How old is the rock? [Given, $\ln (11.3) = 2.425$ ]

The activity of a sample of radioactive material is A1 at time t1 and A2 at time t2t2>t1 . Its mean life is T. Which of the following is correct?

Important Questions on Atoms and Nuclei

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The activity of a sample of radioactive material is $A_{1}$ at time $t_{1}$ and $A_{2}$ at time $t_{2} (t_{2} > t_{1})$ . Its mean life is T. Which of the following is correct?