Certainly! Let's go through the detailed solution step by step for each part of the question.
### (a) Describe the trend in atomic radius as you go down Group 1.
As we look at the given data for some Group 1 elements, we can observe the atomic radius values:
- Lithium (Li): 145 pm
- Sodium (Na): 180 pm
- Potassium (K): 220 pm
- Rubidium (Rb): 235 pm
From these values, we can see a clear trend: The atomic radius increases as we move down Group 1 in the periodic table. This is consistent with the general trend in the periodic table where atomic size increases as we go down a group due to the addition of electron shells.
So, the atomic radius increases as you go down Group 1.
### (b) Predict the melting point of rubidium.
To predict the melting point of rubidium, we can use the known data about atomic radii and melting points for lithium, sodium, and potassium. The known data is as follows:
- Lithium (Li): Melting Point = 181°C, Atomic Radius = 145 pm
- Sodium (Na): Melting Point = 98°C, Atomic Radius = 180 pm
- Potassium (K): Melting Point = 64°C, Atomic Radius = 220 pm
We can determine the relationship between the melting point and the atomic radius by fitting a linear model. The trend can be approximated by a linear equation:
[tex]\[ \text{Melting Point} = m \cdot (\text{Atomic Radius}) + b \][/tex]
By analyzing the given data, the following coefficients for the linear model are obtained:
- The slope ([tex]\(m\)[/tex]) is approximately -1.543
- The intercept ([tex]\(b\)[/tex]) is approximately 394.68
Using these coefficients, we can predict the melting point of rubidium. The atomic radius of rubidium is given as 235 pm. Substituting this value into the linear equation:
[tex]\[ \text{Melting Point of Rubidium} = -1.543 \cdot 235 + 394.68 \][/tex]
[tex]\[ \text{Melting Point of Rubidium} \approx 32.03{}^{\circ} C \][/tex]
Thus, the melting point of rubidium is approximately 32.03°C.
### Summary
(a) The atomic radius increases as you go down Group 1.
(b) The melting point of rubidium is approximately 32.03°C.
