A vacuum chuck for clamping workpieces, in particular wafers, and a measuring device and a method for checking workpieces by way of X-ray fluorescent radiation. The vacuum chuck has a clamping plate having a support surface, having at least one suction connection arranged on a base body for connecting to a negative-pressure device and for clamping the workpiece on the clamping plate by negative pressure received by the base body and having several suction grooves arranged in the clamping plate and are open towards the support surface. The support surface has concentric suction grooves having a suction opening to which a negative-pressure line is connected or which is connected to a work channel. Each suction groove having a separate negative pressure, which is separate to the adjacent suction groove, is selectively controlled by a control valve by a control for supplying the respective negative pressure in the respective suction groove.