The below code snippet explains how to handle RadioButtonList Item click event client side using jQuery
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
    <title></title>
    <script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.8.3/jquery.min.js"></script>
    <script type="text/javascript">
        $("[id*=rbFruits] input").live("click", function () {
            var selectedValue = $(this).val();
            var selectedText = $(this).next().html();
            alert("Selected Text: " + selectedText + " Selected Value: " + selectedValue);
        });
    </script>
</head>
<body>
    <form id="form1" runat="server">
    <asp:RadioButtonList ID="rbFruits" runat="server">
        <asp:ListItem Text="Mango" Value="1" />
        <asp:ListItem Text="Apple" Value="2" />
        <asp:ListItem Text="Banana" Value="3" />
    </asp:RadioButtonList>
    </form>
</body>
</html>
 
 
Explanation:
In the above code snippet there’s an ASP.Net RadioButtonList control rbFruits to which I have assigned a click event handler using the selector [id*=rbFruits] input. When the radio button inside the RadioButtonList control is clicked the jQuery click event is raised and the SelectedText and the SelectedValue of the checked item is displayed in alert box.
 
Demo: