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Question: Predict the density of Cs from the density of following elements. \( K = 0.86gc{m^{ - 3}}\,\,\,\,...

Predict the density of Cs from the density of following elements.
K=0.86gcm−3      Ca=1.548gcm−3   Sc=2.991gcm−3K = 0.86gc{m^{ - 3}}\,\,\,\,\,\,Ca = 1.548gc{m^{ - 3}}\,\,\,Sc = 2.991gc{m^{ - 3}}
Rb=1.532gcm−3  Sr=2.68gcm−3      Y=4.34gcm−3Rb = 1.532gc{m^{ - 3}}\,\,Sr = 2.68gc{m^{ - 3}}\,\,\,\,\,\,Y = 4.34gc{m^{ - 3}}
Cs=?                         Ba=3.51gcm−3     La=6.16gcm−3   Cs = ?\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,Ba = 3.51gc{m^{ - 3}}\,\,\,\,\,La = 6.16gc{m^{ - 3}}\,\,\,

Explanation

Solution

Caesium is an alkali metal with chemical symbol Cs and atomic number 5555 . It belongs to the first group and sixth period of the modern periodic table. Density is the ratio of mass of an element to its volume. As we move down the group or move from left to right along a period, the density of elements increases.

Complete answer:
In the given question, K, Rb and Cs belong to group 11 ,Ca, Sr and Ba belong to group 22 , Sc, Y and La belong to group 33 of the periodic table. Elements show periodicity in their chemical properties. We can observe an increase in the density as we move down a group or move along a period from left to right. To find the density of Cs, let us consider the ratio of densities of elements in a group first.
The ratio of densities of Ba and Sr is, 3.512.68≈1.31\dfrac{{3.51}}{{2.68}} \approx 1.31
The ratio of densities of La and Y is, 6.164.34≈1.42\dfrac{{6.16}}{{4.34}} \approx 1.42
When we subtract both these values, we get 1.42−1.31=0.111.42 - 1.31 = 0.11 .
This suggests that the ratios of densities of Cs and Rb must show a decrement of 0.110.11 from the density ratio values of Ba and Sr.
Therefore, density of Csdensity of Rb=1.31−0.11=1.20\dfrac{{density\,of\,Cs}}{{density\,of\,Rb}} = 1.31 - 0.11 = 1.20
This implies that, density of Cs =1.20×1.532=1.8384gcm−3= 1.20 \times 1.532 = 1.8384gc{m^{ - 3}}
The density of Cs is 1.8384gcm−31.8384gc{m^{ - 3}} .

Note:
The density of Cs at room temperature is 1.93gcm−31.93gc{m^{ - 3}} and at melting point it is 1.843gcm−31.843gc{m^{ - 3}} .
The density of elements increases as we move down the group. Although both mass and volume increases, the rate of increase of mass outweighs the volume rate. In a period, the atomic radius decreases as we move from left to right and thus the volume. Therefore, increase and mass and decrease in volume eventually leads to increase in density along a period.