Atomic numbers of three elements \(E_1, E_2\) and \(E_3\) of periodic table are \(Z_1, 50\) and \(Z_2\) respectively. From the position of the elements shown in figure, the value of \((Z_2 - Z_1)\) is
Show Hint
Use magic numbers to find atomic numbers in groups.
Group 13: B(5) \(\xrightarrow{+8}\) Al(13) \(\xrightarrow{+18}\) Ga(31) \(\xrightarrow{+18}\) In(49) \(\xrightarrow{+32}\) Tl(81).
Group 14: C(6) \(\xrightarrow{+8}\) Si(14) \(\xrightarrow{+18}\) Ge(32) \(\xrightarrow{+18}\) Sn(50).
Group 15: N(7) ... Sb(51) \(\xrightarrow{+32}\) Bi(83).
Step 1: Identify the position of \(E_2\)
\(E_2\) has atomic number 50. This is Tin (Sn).
Position in Periodic Table:
- Group 14 (Carbon family)
- Period 5
Step 2: Determine position of \(E_1\)
The diagram shows \(E_1\) is one step up and one step left relative to \(E_2\).
- Period of \(E_1 = \text{Period of } E_2 - 1 = 5 - 1 = 4\).
- Group of \(E_1 = \text{Group of } E_2 - 1 = 14 - 1 = 13\).
Element in Period 4, Group 13 is Gallium (Ga).
Atomic number \(Z_1 = 31\).
Step 3: Determine position of \(E_3\)
The diagram shows \(E_3\) is one step down and one step right relative to \(E_2\).
- Period of \(E_3 = \text{Period of } E_2 + 1 = 5 + 1 = 6\).
- Group of \(E_3 = \text{Group of } E_2 + 1 = 14 + 1 = 15\).
Element in Period 6, Group 15 is Bismuth (Bi).
Atomic number \(Z_2 = 83\).
Step 4: Calculate \((Z_2 - Z_1)\)
\[ Z_2 - Z_1 = 83 - 31 = 52 \]
Final Answer: 52.
