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Question

The mass of an electron is 9.1×1031 kg while the mass of a proton is 1.67×1027 kg. Which among the proton and electron has the larger mass?

A
Proton
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B
Electron
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C
Both have the same mass
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D
Cannot be determined
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Solution

The correct option is A Proton
Mass of an electron =9.1×1031 kg
Mass of a proton =1.67×1027 kg

First Method–––––––––––––––

Step 1:
Write the numbers in scientific notation. Here, the masses 9.1×1031 kg and 1.67×1027 kg are already in scientific notation.

Step 2:
Compare the exponents of numbers. The larger the exponent, the greater the number.
27>31
1.67×1027>9.1×1031

Therefore, proton has a greater mass than the mass of an electron.

Second Method––––––––––––––––––

We can compare the masses by making the same exponents to the base 10.

We would make the powers of 10 as 31 for both the masses.

For proton's mass 1.67×1027, to make the exponent of 10 as 31, we need to multiply 104 with 1027. And, that we can acheive by moving the decimal point in 1.6700 by 4 units to the right.

Hence,
Mass of an electron =9.1×1031 kg
Mass of a proton =16700×1031 kg

Now, we can compare the masses of electron and proton by comparing the respective coefficients as both the exponents of 10 are equal to 31.

The number with the larger coefficient is greater.

16700>9.1
16700×1031>9.1×1031, i.e., the mass of proton is greater than the mass of an electron.

Therefore, option (a.) is the correct one.

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