Arrange the following metals in the increasing order of their densities. K,Sc, Ti and Ca

Options

A. `K lt Ca lt Sc lt Ti`
B. `Ti lt Sc lt Ca lt K`
C. `Sc lt Ti lt K lt Ca`
D. `Sc lt Ti lt Ca lt K`

Answer

To arrange the metals K (Potassium), Sc (Scandium), Ti (Titanium), and Ca (Calcium) in increasing order of their densities, we need to consider the relationship between atomic mass, atomic size, and density.

### Step-by-Step Solution:

1. **Identify the Metals and Their Atomic Numbers:**
- Potassium (K) - Atomic Number 19
- Calcium (Ca) - Atomic Number 20
- Scandium (Sc) - Atomic Number 21
- Titanium (Ti) - Atomic Number 22

2. **Understand Density:**
Density is defined as mass per unit volume (Density = Mass/Volume). To compare the densities of these metals, we need to consider both their atomic masses and their atomic volumes.

3. **General Trends in Density:**
- As we move from left to right across a period in the periodic table, the atomic mass generally increases while the atomic size decreases due to increased nuclear charge.
- In the case of transition metals (like Sc and Ti), the d-block contraction also plays a role, leading to smaller atomic sizes despite increasing atomic mass.

4. **Estimate the Densities:**
- Potassium (K) has a relatively low density because it is a soft alkali metal with a larger atomic size.
- Calcium (Ca) has a higher density than potassium but is still relatively low compared to transition metals.
- Scandium (Sc) is a transition metal and has a higher density than both K and Ca due to its smaller size and higher mass.
- Titanium (Ti) has the highest density among these metals due to its smaller atomic size and higher atomic mass.

5. **Order the Densities:**
Based on the above analysis, we can arrange the metals in increasing order of their densities:
- K (Potassium) < Ca (Calcium) < Sc (Scandium) < Ti (Titanium)

### Final Answer:
The increasing order of densities is: **K < Ca < Sc < Ti**