Some more bad advice: When the transistor is "on", the voltage across the base-emitter junction is going to be about 1 volt. Where are you measuring this voltage ? Between the transistor base and the resistor Rs, or between the resistor Rs and the arduino pin ? If the former, that's what you would expect to see. Doesn't really explain the 7V though.
The second thing is, you want to limit the current from the arduino to some small value like, say, 20 mA. ( go look it up ). Preferably less. When the signal is on, you will expect to see around 4 volts drop across the resistor. So your resistor needs to be something in the ballpark of 200 ohms.
Third thing is, transistors have some kind of "gain" which is the ratio between the controlled current and the controlling current. You want to control a current of half an amp with a 20 mA base current (say). That's a current gain of 25x. Is that a reasonable expectation with your transistor ? If it isn't, the answer is to use two transistors where the first one controls the base current of the second one. This is often called a "Darlington" circuit or device.
Fourth thing is, when you turn the transistor "off", the current flowing in the solenoid coil of your doorstrike needs somewhere to go. You need to connect a diode across the terminals in the reverse direction so this current has somewhere to go.