Lanthanide contraction refers to the gradual decrease in the ionic radius of the lanthanide series as the atomic number increases, caused by the poor shielding effect of the 4f-electrons. Two important consequences of lanthanide contraction are: 1. Decreasing ionic radii: As the atomic number increases from \( La^{3+} \) to \( Lu^{3+} \), the size of the ions decreases, leading to an increase in the effective nuclear charge experienced by the electrons. This results in a decrease in the ionic radii. 2. Similarity between the 3d and 4d/5d elements: The lanthanide contraction leads to similarities in the properties of the lanthanide elements and the d-block elements in the same period. For example, \( Zr \) (a 4d element) and \( Hf \) (a 5d element) have very similar ionic radii due to the lanthanide contraction.
Thus, the lanthanide contraction results in smaller ionic radii and increased similarities between the properties of lanthanides and d-block elements.
An amount of ₹ 10,000 is put into three investments at the rate of 10%, 12% and 15% per annum. The combined annual income of all three investments is ₹ 1,310, however, the combined annual income of the first and second investments is ₹ 190 short of the income from the third. Use matrix method and find the investment amount in each at the beginning of the year.