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Q.41

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 1237

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Short Answer

You learned in Chapter 41 that the binding energy of the electron in a hydrogen atom is .

a. By how much does the mass decrease when a hydrogen atom is formed from a proton and an electron? Give your answer both in atomic mass units and as a percentage of the mass of the hydrogen atom.

b. By how much does the mass decrease when a helium nucleus is formed from two protons and two neutrons? Give your answer both in atomic mass units and as a percentage of the mass of the helium nucleus.

c. Compare your answers to parts a and b. Why do you hear it said that mass is “lost” in nuclear reactions but not in chemical reactions?

the amount of mass decrease when the hydrogen formed from one electron and one proton is

the percentage of mass difference of hydrogen atom when it formed from one electron

and one proton is

See the step by step solution

Step by Step Solution

Subpart (a) Step 1: Given expression

Bending energy of a nucleus to eject the one nucleon from it is

Here, Is mass difference and c is speed of the light

Step 2: Calculation

The relation between atomic mass unit and is

Rewrite this equation for 1 MeV

substitute

Therefore, the amount of mass decrease when the hydrogen formed from one electron and one proton is 1.46x10-8u

Step 3: Calculation 

Hydrogen atom consist one proton and one electron, so the total mass of the hydrogen atom is,

Here, is mass of electron and is mass of proton.

Substitute for mc and for .

Find the percentage of mass difference of hydrogen atom when it formed from one electron and

One proton can be calculated as follows.

Therefore, the percentage of mass difference of hydrogen atom when it formed from one electron

and one proton is

Step 4: Expression

Mass difference of a nucleus is,

Here, Z is atomic number of the element of nucleus , A is mass number of the nucleus and M is atomic mass of the nucleus

Substitute 2 for Z, 4 for A, for for and for M and solve for the mass difference of helium nucleus,

Therefore, the mass decrease when helium nucleus formed from two protons and two neutrons is 0.

Find the percentage of mass difference of helium nucleus when it formed from two protons and two neutrons can be calculated as follows.

Therefore the percentage of mass difference of helium nucleus when it formed from two protons and two neutrons is

Step 5: Calculation

The formation of hydrogen atom from one electron and one proton is a chemical reaction. The formation of helium nucleus from two protons and two neutrons is a nuclear reaction. From the above two results, in a chemical reaction the loss of mass is negligible. So mass is lost in nuclear reactions but not in chemical reactions.

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