how can I detect whether the android phone in Silent mode programmatically

Use the getRingerMode() method in AudioManager.

AudioManager am = (AudioManager)getSystemService(Context.AUDIO_SERVICE);

switch (am.getRingerMode()) {
    case AudioManager.RINGER_MODE_SILENT:
        Log.i("MyApp","Silent mode");
        break;
    case AudioManager.RINGER_MODE_VIBRATE:
        Log.i("MyApp","Vibrate mode");
        break;
    case AudioManager.RINGER_MODE_NORMAL:
        Log.i("MyApp","Normal mode");
        break;
}