valency-isotopes-and-isobars MCQs for UPSC Prelims

34 practice questions on valency-isotopes-and-isobars from the Journey Inside the Atom section of the UPSC Prelims syllabus. 34 come with a written explanation. Try the sample set below - the answer stays hidden until you ask for it.

11 Easy 16 Medium 7 Hard

Sample questions

Q1
medium
Assertion (A): The average atomic mass of an element is always the simple mean of the masses of its isotopes. Reason (R): Isotopes of an element do not occur in equal proportions in nature.
  1. A Both A and R are true, and R is the correct explanation of A
  2. B Both A and R are true, but R is not the correct explanation of A
  3. C A is true, but R is false
  4. D A is false, but R is true
Show answer and explanation

Correct answer: D - A is false, but R is true

(A) is false: the average atomic mass is a weighted average, and it equals the simple mean only in the special case of equal abundances. (R) is true, and it is exactly the fact that makes (A) false - chlorine, for instance, is about $75\%$ $^{35}\text{Cl}$ and $25\%$ $^{37}\text{Cl}$, so its average is $35.5\ \text{u}$ rather than the simple mean $36\ \text{u}$.
Q2
hard
Three nuclei are described. Y has $17$ protons and $18$ neutrons, Z has $17$ protons and $20$ neutrons, and X has $18$ protons and $19$ neutrons. Which pair are isotopes, and which pair are isobars?
  1. A Y and Z are isobars; Z and X are isotopes
  2. B Y and Z are isotopes; Z and X are isobars
  3. C All three are isotopes of a single element
  4. D Y and X are isotopes; Y and Z are isobars
Show answer and explanation

Correct answer: B - Y and Z are isotopes; Z and X are isobars

Y and Z both have $17$ protons, so they are the same element with mass numbers $35$ and $37$, which makes them isotopes. Z and X have mass numbers $37$ and $37$ but proton counts of $17$ and $18$, so they are different elements sharing a mass number, which makes them isobars. Y and X share neither their proton count nor their mass number of $35$ and $37$.
Q3
hard
A neutral atom of an element has $17$ electrons. Work out its electronic configuration and then its valency.
  1. A $2,8,7$, giving a valency of $1$
  2. B $2,7,8$, giving a valency of $1$
  3. C $2,8,7$, giving a valency of $8$
  4. D $2,8,7$, giving a valency of $7$
Show answer and explanation

Correct answer: A - $2,8,7$, giving a valency of $1$

The shells fill as $2,8,7$, so seven electrons lie in the outermost shell and just one more completes it; gaining that one is far easier than giving away seven, so the valency is $1$. A valency of $7$ counts the valence electrons instead of the electrons needed. The arrangement $2,7,8$ starts the M-shell before the L-shell is full, which the filling rule forbids.
Q4
easy
The two isotopes of chlorine have masses $35\ \text{u}$ and $37\ \text{u}$. A student adds these and divides by $2$ to get $36\ \text{u}$. Why is $36\ \text{u}$ not the average atomic mass of chlorine?
  1. A Because $35$ and $37$ are mass numbers rather than masses, so they may not be added together.
  2. B Because the two isotopes are not equally common; about $75\%$ of chlorine atoms are the $35\ \text{u}$ kind and about $25\%$ are the $37\ \text{u}$ kind.
  3. C Because the two isotopes of chlorine contain different numbers of protons, so their masses cannot be averaged.
  4. D Because an average atomic mass must be the mass of some real atom, and no chlorine atom has a mass of $36\ \text{u}$.
Show answer and explanation

Correct answer: B - Because the two isotopes are not equally common; about $75\%$ of chlorine atoms are the $35\ \text{u}$ kind and about $25\%$ are the $37\ \text{u}$ kind.

A simple mean silently assumes the isotopes occur in equal numbers, but chlorine is about three-quarters $^{35}\text{Cl}$, so the true average $35.5\ \text{u}$ is pulled towards the lighter isotope. Isotopes of one element always have the same number of protons and differ only in neutrons. An average atomic mass need not match any real atom, which is why $35.5\ \text{u}$ is accepted. Mass numbers do count the nucleons and can certainly be combined.
Q5
medium
A sample of $1000$ atoms of an element is found to contain $600$ atoms of mass $24\ \text{u}$ and $400$ atoms of mass $26\ \text{u}$. What is the average atomic mass of this element?
  1. A $25.2\ \text{u}$
  2. B $24\ \text{u}$
  3. C $24.8\ \text{u}$
  4. D $25\ \text{u}$
Show answer and explanation

Correct answer: C - $24.8\ \text{u}$

The total mass of the sample is $600 \times 24 + 400 \times 26 = 24800\ \text{u}$, and sharing that over $1000$ atoms gives $24.8\ \text{u}$ per atom. The value $25\ \text{u}$ is the simple mean of $24$ and $26$, correct only if the two kinds of atom were equal in number. The value $25.2\ \text{u}$ comes from giving the $26\ \text{u}$ atoms the count of $600$. Quoting $24\ \text{u}$ names the commoner atom instead of averaging.
Q6
hard
An element has exactly two isotopes, of mass $20\ \text{u}$ and $22\ \text{u}$, and its average atomic mass is $20.4\ \text{u}$. What percentage of its atoms are the $22\ \text{u}$ isotope?
  1. A $80\%$
  2. B $20\%$
  3. C $40\%$
  4. D $50\%$
Show answer and explanation

Correct answer: B - $20\%$

Every $22\ \text{u}$ atom lifts the average $2\ \text{u}$ above the $20\ \text{u}$ base, and the average is lifted by only $0.4\ \text{u}$, so the heavier isotope is $0.4/2 = 0.2$ of the atoms, that is $20\%$. A check confirms it: $(20 \times 80 + 22 \times 20)/100 = 20.4\ \text{u}$. Reading the $0.4$ straight off as $40\%$ gives $20.8\ \text{u}$, equal shares give $21\ \text{u}$, and $80\%$ heavy atoms give $21.6\ \text{u}$.
Q7
medium
Assertion (A): Atoms of calcium, potassium and argon that all have mass number $40$ are isotopes of one another. Reason (R): Atoms of different elements that share the same mass number are called isobars.
  1. A Both A and R are true, and R is the correct explanation of A
  2. B Both A and R are true, but R is not the correct explanation of A
  3. C A is true, but R is false
  4. D A is false, but R is true
Show answer and explanation

Correct answer: D - A is false, but R is true

(A) is false: calcium, potassium and argon have atomic numbers $20$, $19$ and $18$, so they are different elements and cannot be isotopes of one another. (R) is the correct definition of isobars, and it is exactly the word that should have been used in the assertion.
Q8
hard
A carbon atom has four electrons in its outermost shell, and it can neither lose nor gain four electrons easily. How does a carbon atom complete its outermost shell, and what valency does this give it?
  1. A It shares just one electron, giving it a valency of $1$
  2. B It loses all four of them, giving it a valency of $4$
  3. C It gains four more, giving it a valency of $0$
  4. D It shares four electrons with other atoms, giving it a valency of $4$
Show answer and explanation

Correct answer: D - It shares four electrons with other atoms, giving it a valency of $4$

With exactly four valence electrons, carbon sits halfway between losing and gaining, so it completes its shell by sharing four electrons, and the number shared is its valency, $4$. Losing or gaining four electrons is the difficulty the question rules out. Gaining electrons could never give a valency of zero, and sharing only one would leave the shell far from complete.

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