Question:

The percentage of radioactive substance left after 5 half lives is

Updated On: Jul 7, 2022
  • 0.31
  • 0.03125
  • 0.003
  • 0.01
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The Correct Option is B

Solution and Explanation

$\frac{N}{N_0} = \left( \frac{1}{2} \right)^5 = \frac{1}{32} = \frac{1}{3^2} = M \frac{100}{32}% = 3.125%$
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Concepts Used:

Mole Concept

In the field of chemistry, a mole is defined as the amount of a substance that contains exactly 6.02214076 * 1023 β€˜elementary entities’ of the given substance.

The number 6.02214076*1023 is popularly known as the Avogadro constant and is often denoted by the symbol β€˜NA’. The elementary entities that can be represented in moles can be atoms, molecules, monoatomic/polyatomic ions, and other particles (such as electrons).

For example, one mole of a pure carbon-12 (12C) sample will have a mass of exactly 12 grams and will contain 6.02214076*1023 (NA) number of 12C atoms. The number of moles of a substance in a given pure sample can be represented by the following formula:

n = N/NA

Where n is the number of moles of the substance (or elementary entity), N is the total number of elementary entities in the sample, and NA is the Avogadro constant.

The word β€œmole” was introduced around the year 1896 by the German chemist Wilhelm Ostwald, who derived the term from the Latin word moles meaning a β€˜heap’ or β€˜pile.

The mole concept refers to the atomic mass of a mole that is measured in grams. The gram atomic mass of an element is known as a mole. The mole concept combines the mass of a single atom or molecule in a.m.u. to the mass of a large group of comparable molecules in grams. Atomic mass is the mass of a single atom, whereas molecular mass is the mass of a group of atoms. 

The Formula of Mole Concept

The number of units that make up a mole has been calculated to be 6.022 Γ—10Β²Β³. The fundamental constant is also known as Avogadro's number (NA) or Avogadro constant. This constant is appropriately represented in chemistry using an explicit unit termed per mole.

Number of Moles = (Mass of the Sample)/(Molar Mass)

Read More: Mole Fraction