[Solved] Einstein's mass-energy relation emerging out of his famous theory of relativity relates mass (m) to energy (E) as E=mc2, where c is speed of light in vacuum. At the nuclear level, the magnitudes of energy are very small. The energy at nuclear level is usually measured in MeV, where 1MeV=1.6×10−13 J; the masses are measured in unified atomic mass unit (u) where, 1u=1.67×10−27 kg.(a) Show that the energy equivalent of 1u is 931.5MeV.(b) A student writes the relation as 1u=931.5MeV. The teacher points out that the relation is dimensionally incorrect. Write the correct relation. - Physics Exemplar

Uploaded: 2022-09-22T06:47:34.000Z
Duration: 6 min

(a) We know that1amuE=1u=1.67×10−27 kg=mc2 Energy E=E=(1.67×10−27)(3×108)2 J=1.67×9×10−11 J=1.6×10−131.67×9×10−11MeV=939.4MeV≈931.5MeV (b) The dimensionally correct relation is1amu×c2=1u×c2=931.5MeV

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Einstein's mass-energy relation emerging out of his famous the

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Class 11

NCERT Exemplar

Chapter 1: Units and Measurements

44 questions

(a) How many astronomical units (AU) make 1 parsec?
(b) Consider a sunlike star at a distance of 2 parsecs. When it is seen through a telescope with 100 magnification, what should be the angular size of the star? Sun appears to be

(1/2)^{\circ}

from the earth. Due to atmospheric fluctuations, eye cannot resolve objects smaller than 1 arc minute.
(c) Mars has approximately half of the earth's diameter. When it is closest to the earth it is at about

1/2 AU

from the earth. Calculate what size it will appear when seen through the same telescope.

Einstein's mass-energy relation emerging out of his famous theory of relativity relates mass

(m)

to energy

(E)

E = m c^{2}

, where

c

is speed of light in vacuum. At the nuclear level, the magnitudes of energy are very small. The energy at nuclear level is usually measured in

MeV

, where

1 MeV = 1.6 \times 1 0^{- 13} J

; the masses are measured in unified atomic mass unit

(u)

where,

1 u = 1.67 \times 1 0^{- 27} kg

.(a) Show that the energy equivalent of

1 u

931.5 MeV

.
(b) A student writes the relation as

1 u = 931.5 MeV

. The teacher points out that the relation is dimensionally incorrect. Write the correct relation.

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Question

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Solving time: 3 mins

Einstein's mass-energy relation emerging out of his famous theory of relativity relates mass $(m)$ to energy $(E)$ as $E = m c^{2}$ , where $c$ is speed of light in vacuum. At the nuclear level, the magnitudes of energy are very small. The energy at nuclear level is usually measured in $MeV$ , where $1 MeV = 1.6 \times 1 0^{- 13} J$ ; the masses are measured in unified atomic mass unit $(u)$ where, $1 u = 1.67 \times 1 0^{- 27} kg$ .(a) Show that the energy equivalent of $1 u$ is $931.5 MeV$ .
(b) A student writes the relation as $1 u = 931.5 MeV$ . The teacher points out that the relation is dimensionally incorrect. Write the correct relation.

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Updated on: Sep 22, 2022

Book:

Physics Exemplar (NCERT Exemplar)

Text solutionVerified

(a) We know that

1 amu E = 1 u = 1.67 \times 1 0^{- 27} kg = m c^{2}

Energy E = E = (1.67 \times 1 0^{- 27}) (3 \times 1 0^{8})^{2} J = 1.67 \times 9 \times 1 0^{- 11} J = \frac{1.67 \times 9 \times 1 0 ^{- 11}}{1.6 \times 1 0 ^{- 13}} MeV = 939.4 MeV \approx 931.5 MeV

(b) The dimensionally correct relation is

1 amu \times c^{2} = 1 u \times c^{2} = 931.5 MeV

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Einstein's mass-energy relation emerging out of his famous theory of relativity relates mass

(m)

to energy

(E)

E = m c^{2}

, where

c

is speed of light in vacuum. At the nuclear level, the magnitudes of energy are very small. The energy at nuclear level is usually measured in

MeV

, where

1 MeV = 1.6 \times 1 0^{- 13} J

; the masses are measured in unified atomic mass unit

(u)

where,

1 u = 1.67 \times 1 0^{- 27} kg

.(a) Show that the energy equivalent of

1 u

931.5 MeV

.
(b) A student writes the relation as

1 u = 931.5 MeV

. The teacher points out that the relation is dimensionally incorrect. Write the correct relation.

15 mins ago

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Practice more questions from Physics Exemplar (NCERT Exemplar)

(1/2)^{\circ}

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from the earth. Calculate what size it will appear when seen through the same telescope.

Einstein's mass-energy relation emerging out of his famous theory of relativity relates mass

(m)

to energy

(E)

E = m c^{2}

, where

c

is speed of light in vacuum. At the nuclear level, the magnitudes of energy are very small. The energy at nuclear level is usually measured in

MeV

, where

1 MeV = 1.6 \times 1 0^{- 13} J

; the masses are measured in unified atomic mass unit

(u)

where,

1 u = 1.67 \times 1 0^{- 27} kg

.(a) Show that the energy equivalent of

1 u

931.5 MeV

.
(b) A student writes the relation as

1 u = 931.5 MeV

. The teacher points out that the relation is dimensionally incorrect. Write the correct relation.

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Question Text	Einstein's mass-energy relation emerging out of his famous theory of relativity relates mass $(m)$ to energy $(E)$ as $E = m c^{2}$ , where $c$ is speed of light in vacuum. At the nuclear level, the magnitudes of energy are very small. The energy at nuclear level is usually measured in $MeV$ , where $1 MeV = 1.6 \times 1 0^{- 13} J$ ; the masses are measured in unified atomic mass unit $(u)$ where, $1 u = 1.67 \times 1 0^{- 27} kg$ .(a) Show that the energy equivalent of $1 u$ is $931.5 MeV$ . (b) A student writes the relation as $1 u = 931.5 MeV$ . The teacher points out that the relation is dimensionally incorrect. Write the correct relation.
Updated On	Sep 22, 2022
Topic	Units and Measurements
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 2
Upvotes	313
Avg. Video Duration	10 min

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