To determine which ion is isoelectronic with carbon monoxide (CO), we need to first find the number of electrons in each species. Isoelectronic species have the same number of electrons.
CO is composed of one carbon atom and one oxygen atom. Carbon (C) has an atomic number of 6, and oxygen (O) has an atomic number of 8. Therefore, the total electron count in CO is:
Total electrons in CO = \(6 \text{ (carbon)} + 8 \text{ (oxygen)} = 14\) electrons.
Let's analyze each option:
1. \( \text{O}_2^+ \)
Oxygen molecule \( \text{O}_2 \) has \( 8 + 8 = 16 \) electrons. Loss of one electron (indicated by \( + \)) gives:
Total electrons in \( \text{O}_2^+ \) = 16 - 1 = 15 electrons.
2. \( \text{CN}^- \)
Cyanide ion \( \text{CN}^- \) consists of carbon (6 electrons) and nitrogen (7 electrons) with an additional electron due to the negative charge:
Total electrons in \( \text{CN}^- \) = 6 + 7 + 1 = 14 electrons.
3. \( \text{O}_2^- \)
\( \text{O}_2 \) molecule again starts with 16 electrons. With an additional electron (indicated by \( - \)):
Total electrons in \( \text{O}_2^- \) = 16 + 1 = 17 electrons.
4. \( \text{N}_2^+ \)
\( \text{N}_2 \) molecule consists of \( 7 + 7 = 14 \) electrons. Loss of one electron (indicated by \( + \)) gives:
Total electrons in \( \text{N}_2^+ \) = 14 - 1 = 13 electrons.
Thus, the ion with the same number of electrons as CO (14 electrons) is \( \text{CN}^- \).
A solid cylinder of mass 2 kg and radius 0.2 m is rotating about its own axis without friction with angular velocity 5 rad/s. A particle of mass 1 kg moving with a velocity of 5 m/s strikes the cylinder and sticks to it as shown in figure.
The angular velocity of the system after the particle sticks to it will be: